Personally, I think Mass Effect's kind of been coasting ever since part 2.
Don't get me wrong, they're not terrible games, and there's a lot to like, but I do think the OP is right in saying that it does seem to have gotten this reputation among fans as being not just a great sci-fi game, but some kind of high-point of science fiction of the last 30 years.
Honestly, I can't help but groan a little whenever people mention how great the story of the series is. As a unified three-act structure, it simply isn't all that coherent or well paced. Stories told over several instalments have to stagger events so that everything proceeds smoothly over the course of the entire series. Mass Effect doesn't do that. It front-loads its first instalment with narrative, largely takes a large step sidewards and backwards in part two, then races to the finish line in part three to make up for the lack of distance covered in part 2.
Now, there are certainly individual elements of the overall story that are very well done, such as the Genophage. But there are also large elements of the story that are really quite crap, such as the Human Reaper finale to ME2, and every single thing about Kai-Leng in ME3. Or, perhaps more importantly, the fact that Shepard has no clear progressive arc across the 3 games: in the first game he's fighting against Cerberus. In the second game he's inexplicably killed off, then brought back to life and sides with Cerberus for the most arbitrary reasons, introducing a whole host of headscratching moments and plot-holes in doing so. Then, in the third game, he switches sides again and is back to fighting Cerberus.
It's kind of like if in Lord Of The Rings, Frodo started out on his quest to destroy the Ring in Fellowship, then decided in Two Towers to surreptitiously work for Saruman instead, doing all sorts of secret dirty work for the evil wizard, only to flip the bird at him in Return Of The King and race to Mordor to destroy the Ring in record time. Regardless of whether you want to be 'paragon' or 'renegade' the whole thing is just inconsistent. True Paragons would never join as quasi-fascist an organisation as Cerberus in the first place, and true Renegades would never want to leave once they joined.
I think there's a couple of things that the Mass Effect series has been riding on as a whole:
1) The legacy of the first game. The first game was by far the one with the strongest, most cohesive and consistent narrative. It had a clear arc to it, a very well done premise, and packed in some very well executed moments that people are still talking about to this day, such as being forced to choose between one of your two squadmates. Both ME2 and ME3 had deeply, deeply flawed narratives in comparison. The way ME2 shanghai's Shepard into joining Cerberus I've already covered, and the same with the Human Reaper ending (so, so much derp in that ending). As for ME3, even without the ending fiasco, it features an incredibly badly written, frustrating antagonist (Kai-Leng), and essentially boils down to a Deus Ex Machina to resolve the plot. Creating an enemy as overbearingly evil and mighty as the Reapers only works when you can find a natural cohesive way to overcome their threat. Making up a MacGuffin without any prior referencing in earlier games that is magically able to wipe out the Reaper threat is not good writing. It's what you do when you've written yourself into a corner.
When it comes to overall narrative strength, it's only really the first game that manages to bar up to scrutiny, and I think it's because of the first game that fans have remained as dedicated as they have. If the series had started with a narrative as wonky as ME2's, it would have never picked up the kind of reception it has.
2) The increased emphasis on sex. No, sorry, I'm going to argue this one. The first Mass Effect included romance sideplots without focusing unduly on them. You had the choice to hook up with your party members, but they still existed as characters whether or not you forced your tongue down their throat. But starting with 2, Bioware started to specifically define the characters based on whether you could bone them or not. Sure, they had tragic backstories and snarky one-liners, but seemingly everything from the writing to the marketing focused on the idea that Commander Shepard is a bonafide space-pimp, and everyone in your party has the hots for you. Mass Effect went from being a throw-back to classic Space opera fiction to being a chance for sweaty palmed teenagers to shag their way round the galaxy.
You can tell simply by how noticing how many people's recollections of the latter 2 ME games revolved around which character they hooked up with or wanted to hook up with (Tali and Garrus being the most commonly mentioned). ME 2 is basically one giant game of blind date, with Shepard being presented with a selection of possible characters that he can knock boots with. The actual narrative, the plot relevant stuff carried over from the first game, is pretty poor, and it's not much better in the third game.
This is why I don't have a lot of love for the ME franchise. It was a series that started off focusing on big ideas and themes, and it gradually morphed into simply seeing how many woobie characters Bioware could fit into one game. For all that Bioware said from the outset that they were planning it as a trilogy, it seems to me that they simply didn't write out enough of their narrative from the start, and instead just decided to make it up as they went along. And when compared to the storytelling brilliance that other recent sci-fi such as Battlestar Galactica have managed to maintain across their entire span, for me that simply doesn't cut the mustard.
Of course, all this is IMO, so please don't take this as me trying to spout objective reasoning and gospel truth.