Welcome to the Forums. Sadly, I disagree with you on a lot of things.
First, let me establish something: Mass Effect is a Role Playing Series.
That might seem obvious, but a few of your points ignore this completely. When you play Shepard, you aren't doing the same sort of thing as when you play Master Chief in Halo, Blackburn from BF3, Raynor in SC2 - you are playing a character of your own forging. It is not Bioware's character, it is yours. This is evident from the number of decisions you make about your character, from the basic 'What do you look like?' to covering philosophical issues such as religion. You are given choice as to how you enact, and Shepard's attitude, who they are, and what they will and will not do, has never been dictated by Bioware. Well, until ME3.
In ME3, most of your dialogue is chosen for you. You don't get to choose how your Shepard reacts to things. The Dream sequences you mentioned would not occur for some Shepards - yet they are forced to because Bioware wanted Shepard to be haunted by that. I can honestly say my Shepard doesn't give two s***s about that kid down on Earth, or anybody for that matter. Yet suddenly, they are forced to because Bioware decided they should. This also carries through to the endings. There is no choice to even try to stand against the Reapers [A point which I will discuss more later on], there is only the Diabolus Ex Machinas that the Catalyst presents you. This element of choice is taken away from you, and you are left to make a decision not for your own Shepard, but for the Shepard Bioware envisioned. No legitimacy is given to a Shepard that does nothing, merely a game over screen. This may not seem like a problem, but it ties into the free will theme - which has existed throughout the series - and would, if you are correct in your assumptions of the Reaper's strength, be the 'Reapers win' ending we were promised by Devs.
Next, I would like to address the 'Free Will' theme. Whilst you may not have noticed it, it has always been prominent in the series. Think back to the final fight of ME1. What was the first half of it? A conversation with Saren. What was that conversation about? The same thing that had been discussed before, both with Saren and with others on Virmire - Indoctrination. Half of the final fight in Mass Effect 1 is about free will. Can Saren break through the control established by Sovereign, regain his free will, and then sacrifice himself for the greater good?
Fast Forward to ME2. What is something Miranda tells you about your resurrection? She wanted to plant a control chip in you - to take away your free will. This is used to paint a positive light on the Illusive man, as he prevented her from doing so.
Then into ME3, what was the final fight? No, it wasn't Marauder Shields. It was a conversation with the Illusive man about controlling the Reapers, and again, indoctrination. Can you break through and convince him that he is being controlled. Can he regain his free will and sacrifice himself, or is he still beholden to the Reapers?
The Indoctrination theme has been strong running in the series right from the first game, and is all about free will. Free will is a theme expressed in Mass Effect through both the gameplay and through the narrative, and is even more important a theme because of this.
Now, on to your points:
1. Sacrifice for the greater good.
As you have noticed, this theme has been prominent throughout all of Mass Effect. There are two problems with it in ME3 though: That it affects Shepard, and how that is handled.
The first part of this problem is that Shepard themselves is now affected by this. Whilst you believe them not being affected by this would destroy the theme, I think you are utterly wrong in this regard. Simply because others sacrifice themselves does not mean you must. If your three friends threw themselves infront of a bus in a futile attempt to stop it from hitting an old lady, would you HAVE to jump infront of that same bus? Would there be no sacrifice if you didn't?
No. This paragraph of yours illustrates it perfectly:
Quite frankly it seems almost ridiculous to even go through all the examples because they are so numerous, so I'm going to just list them: (1) Sacrificing people on Earth while you escape, (2) Tali (if you side with the Geth and can't unite the races), (3) Kaiden/Ashley (if you can't get them to back down), (4) Thane (saving the council), (5) Anderson (staying on Earth to lead the resistance), (6) Primarch's son (stopping the bomb), (7) the entire quarian race (if you side with geth), (8) entire geth race (if you side with the quarians), (9) Thessia. These are just the main ones, there are times of smaller tales of sacrifice for the greater good such as the Krogan dying on the Rachni planet, or the Rachni queen dying if the Krogan team is saved.
All throughout the game sacrifice is rife. The theme runs strong. You suggest that if Shepard didn't die, the theme would be destroyed. I disagree.
Was the theme destroyed in ME1 because Shepard didn't die to stop Saren and Sovereign?
Was it destroyed in ME2 because you had to REALLY screw up for Shepard to die to stop the Collectors?
If you answered no to either of the above, there is no reason for it to be forced now. This part of the problem is the minor part however. The major part is how Shepard's death is handled.
The handling of Shepards death is nothing short of atrocious. Imagine LOTR, the ring has fallen into the lava, but it doesn't get destroyed. Suddenly, Sauron laughs and says Frodo must jump into the lava and sacrifice himself for the Ring to be destroyed. Imagine Star Wars, once the Emperor is dead Vader reveals to Luke that the new Deathstar can only be destroyed if he jumps into its core, and it is otherwise invulnerable.
These would be terrible ways to end those stories. There is no reason for the main protagonist to die, yet the death is forced. This same problem occurs in the Mass Effect 3 endings. A Diabolus Ex Machina is enacted to force the main character's death, without any real reason given for why this must be the case. Many people would not have cared so much if we saw the Normandy do a suicide run, ramming Harbinger to try and give Shepard a chance to reach the Conduit. We wouldn't have cared had we seen our squadmates die under Reaper fire as they tried to allow us passage. We wouldn't have cared had Shepard died fighting, or had been killed by Harbinger as he activated the Crucible, or had the Illusive man come back in husk form and shot him in the back, before the Catalyst destroyed it [A bit of a push with that one though]. Why? There is a quantifiable reason for Shepard and the Squad's death. To stop the Reapers from achieving their goals, or because they were caught off guard.
In the ME3 endings, we have no such reason for Shepard's death. 'You must jump into a beam of light and be obliterated', 'Why?'. 'Because your DNA will fuel the creation of synthesis!'. 'Can I make a blood donation instead? You know, enough of my DNA is already splattered over this station, and I could send a bit more through. No reason I have to die thought'. 'Yes, you must die'. 'Why?'. 'Because... You must'.
'You will dissolve into nothingness upon grasping those handles'. 'Why?'. 'Because you must die, no other reason'.
'An explosion will kill you when you shoot that power conduit'. 'Well, I'll just line up a shot from here then...'. 'You can't'. 'Why not?'. 'You must be within the explosion's range'. 'Why?'. 'Because you must die'.
Out of the lot, Synthesis is the best explained, but it is still sketchy at best. Why does Shepard need to die to activate the Crucible? Why is there no conventional means to do so?
The game turns something that should occur normally into something that the character must die for. In this case it is most equivalent to a gun that requires the user to shoot themselves in the head, and it will then kill their target. Why? No reason given. The user must die, that's all you need to know.
Had Shepard died through a means that made sense - KIA by Reaper forces, by Harbinger, by an Illusive man Husk - many wouldn't have minded so much. They would still be upset about the mistake that was Shepard's death, but it would not be as important a point in their minds had the reasons for Shepard's death been not so non-existent.
You also bring up the "Hero's journey" argument, though in somewhat the wrong context. You will find that when people use this argument, they don't refer to wanting Shepard to live, the are referring to the utter failure to follow this narrative structure in the end of ME3. The game ends on its climax. There are few, if any, works that do this successfully, and ME3 isn't one of them. There is no 'Return with the Elixir' stage, the game ends on its climax. There is no resolution or closure, only the climax. This utter failure to follow the narrative structure that has been used throughout the rest of the series - both collectively, each game individually, and often each mission individually as well - is what people refer to as one of the literary failings of the ME3 ending.
2. Entropy. This you have split into two parts: The cycles in the story, and the reasons the Reapers can't be beaten. I will address both.
Firstly, the cycles. Whilst it is undeniable that these cycles exist, what many object to is the assertion that Organics and Synthetics will ALWAYS be at war, and ALWAYS try to kill each other, and even then, that synthetics will ALWAYS win.
All such ideas are destroyed in ME3. Firstly, that organics and synthetics will always be at war. It is easy to see how this is wrong: The Quarians and Geth united, EDI hooking up with Joker. Synthetics and organics are not always trying to kill each other, and are not always at war. This is one of the main parts of the game - disproving such an assertion. The entire Rannoch segment of ME3, and Legion from ME2 - are made pointless by the end, as their message is utterly revoked by the Catalyst, who claims that such things cannot happen.
Then, lets assume that the Quarians and Geth had kept on fighting. Who would have won? Thanks to the Reapers, likely the Geth. Lets take the Reapers out of the equation though, considering their purpose is to protect organics by killing them. Who would have won? The Quarians, easily. Without the Reaper code, the Geth are utterly outgunned by the Quarians, and are wiped out. The technological singularity point is revoked.
In the Prothean's cycle, the galaxy was united to defeat AI. It is implied that the Organics began to win. Then the Reapers showed up.
For the Reapers' purpose being to protect organics, they seem to put more effort into protecting synthetics
Whilst it may be true that synthetics and organics will eventually go to war, the Reapers do nothing to prevent this - they actually encourage it - and in doing so are both the cause for such wars, and the failed 'solution' to them.
Secondly, the fact that the galaxy can not defeat the Reapers. This is never hinted at throughout any of the games. What is hinted at is that we can not defeat them alone. I ask you though, is the Systems Alliance alone in this fight? Or do they have the support of Krogan, Turian, Salarian, Asari, Batarian, Volus, Elcor, the Blue Suns, Eclipse, Blood Pack, Ex Cerberus Operatives and more. This is a threat that the Reapers have never faced before - a fact that you seem to forget.
It is established in ME1 that the only reason the Reapers are so successful is because they catch their enemies completely off guard. Not off guard in a 'You didn't believe we were real, so now Palavan is burning' way, but in a 'You didn't know we existed, so we jumped through the Citadel Relay, destroyed your government, shut down the entire relay network then picked you off one by one' way. They have never before faced the combined might of the galaxy in one fight.
Yes, the Reapers are strong. We, however, are stronger. The Reaper forces are spread across the Galaxy - not just at Earth - and whilst what is at Earth is the largest concentration of their forces, it is nowhere near all of them. Four Dreadnoughts can destroy one Reaper capital ship. We have over 100. A handful of cruisers and frigates can take down a Reaper Destroyer - we have thousands. These numbers are based off conventional Mass Accelerator weaponry. Most fleets have been equipped with Thannix Heat Based Weaponry - which is even more effective vs the Reapers. It would be perfectly possible to defeat the Reaper fleet at Earth - if you had the entire galaxy behind you. Heavy losses would be inevitable, but heavier losses would be inflicted on the Reapers. In addition to our superior numbers, what effect does taking out an enemy ship have for each fleet? If you take out a Sword/Shield Frigate or Cruiser, you are making a minimal impact on the overall firepower of Sword. You take out a Dreadnought, you are making a small impact on the overall firepower. You take out one Reaper Destroyer, you've taken a small amount of firepower away. Take out a Capital ship, you've taken a relatively large amount of firepower away. Each casualty inflicted on the Reapers gains Sword an even greater advantage than it had before.
The Reapers are far from unbeatable. We have them fighting us on relatively easy ground - for the first time in the history of the galaxy - and our fleet is actually stronger than theirs - at Earth, if you did everything right.
3. Finally, the ending in relation to Forgiveness. This largely ties into what I said earlier about this being a Role Playing Game, not a linear game. You are playing your Shepard, not Bioware's.
You state that Shepard feels guilty about the losses of all those left behind - but what do you base your evidence on? What YOUR Shepard felt, and the dreams that we were forced into. My Shepard is a survivor. If there is a cost that can be taken to save themself, they'll do it. This is galactic war, and whilst it would be nice to save everyone, Shepard for me feels that the most important person to save is themself. There is no guilt about Thessia. There is anger that he failed, and anger that the councillor hadn't told him about this sooner, but no guilt. Likewise, my Shepard felt no guilt for that kid. It was one kid out of billions that died during this war, and he was more concerned with whether Anderson made it out, or whether the Normandy would become that Reaper's next target.
This is one of the big failings of the third game on the whole - it takes away a lot of that role playing aspect, and forces Shepard to become the character that Bioware want them to be. This is extremely evident in the ending where Shepard literally just gives up. There is no fight. There is no 'What if you're lying to me?'. There is nothing but pure acceptance and defeatism. The only thing I can think of that would be going through Shepard's head is 'Damn, we lost, and now I die because some stupid hologram is telling me to. F***'.
My Shepard ain't a Paragon, he don't give two sh**s about who he has to sacrifice to win this war - so long as its not himself. This isn't a choice that Bioware should get to make, especially when they've established this as a Role Playing Game, where Shepard is your Shepard, and they've put forward numerous promises about what the ending could be. This is why ME3 is, by my standards, the worst game in the series. Its combat is better than 1 and two, as is its ability system and arguably the inventory too, but in the role playing department it falls way behind. Shepard is no longer your Shepard, they're Bioware's Shepard.
Mass Effect 3's ending is neither a great, nor the greatest ending. It barely even qualifies for 'OK'. You have addressed few of the many issues that people find with it. Things such as plot holes, the literary failings of the ending, the lack of choice, broken developer promises, destruction of Shepard as a character, random space magic, diabolous ex machina, no closure - the ending is plainly bad.
I will direct you to read a few articles on this. For example:
http://jmstevenson.wordpress.com/2012/03/22/all-that-matters-is-the-ending-part-2-mass-effect-3/
http://social.bioware.com/forum/1/topic/355/index/10056886
and watch this:
http://www.youtube.com/watch?v=7MlatxLP-xs
There are a ton of things wrong with the endings. They are not great. They are not good. They are barely mediocre. They spit on the ideas formed by the rest of the series - not simply narrative ideas such as the Free Will theme, but also Role Playing ideas, and the idea that Shepard is your character. The ending is a failure when all is taken into account. It does not accomplish its purpose. It is literarily unsound. It takes the key ideas established in the gameplay of the series, and some of the narrative ideas, and throws them out the window. It disregards everything that the Mass Effect franchise stood for, and that is why people hate it.