Read this carefully, it will likely be long.
This article pretty much defines the differance between magic in horror and magic in fantasy which is why they tend to be seperate generes. To put things into a PnP RPG context, something like Call Of Cthulhu uses more of a basis of real occultism for some of the "general" stuff, but real power tends to come from dealing with dark forces that generally exact a huge toll on the person casting the spells. Solutions in fighting the supernatural with the supernatural tend to revolve more on invoking one being or power to counter another, with the caster being destroyed body and mind in the process as a matter of course. Such a concept of magic doesn't play well with the sword and sorcery "magic is just another power to be used" school so such RPGs tend to be kept very seperate. The horror of say CoC is that humanity is irrelevent supernaturally speaking, and the idea of people with their own powers plays havoc with the concept. This is why when you see crossovers Cthulhu and company just become another demon to be punched/blasted when you start seeing characters who are powerful in their own right. That said when it comes to RPGs, either computer or PnP the reason why you don't see too much in the way of "historical accuracy" especially in games trying to be dark, is fear of offending someone. Personally I don't give it much credence and think most other people shouldn't either, but basically when you consider dealing with things that some people consider real, it's offensive for everyone else to label them as fantasy and say "it's fun to play a game where we pretend this is real". Not to mention the whole can of worms that is the political correctness movement, and the whole new age thing, getting into Witchcraft alone can start some nasty arguements given that today people like to embrace the new-age re-invention as the truth and pretend the Celts, Gauls, etc... were all a bunch of hippies dancing around in the moonlight. When you get into the Native American stuff, that can get pretty gruesome (I worked for two differant Indian Tribes) but again, it's not PC, it goes to a similar place
as the New Age.
That said regular fantasy is not a genere for everyone, personally I like it, but I've met more than a few people who share the sentiments of the article writer. Other than Call Of Cthulhu there have been several "Dark" Fantasy games that have tried to get into low magic settings, or ones with hugely dark and evil spellcasting systems that generally screwed the caster (or put them in jeopardy), without getting into real history as a basis to avoid offending anyone. One recurring example is attempts to do Michael Moorcock's writings as an RPG, there have been a few differant editions of "Stormbringer", which has also seen incarnations as "Elric!", and even D20 printings of things like "Dragon Lords Of Melnibone". To put it bluntly in that setting being a spellcaster means pledging yourself to chaos, and needing to deal with demons (the stuff of pure chaos) to get them to assume the form of items and such. The backlash involved can be epic to put it lightly.
Overall though most of this comes down to "deconstructionism" and like most deconstructionist arguements it falls apart rather quickly when you try and assert it as some kind of logic, rather than personal preferance. To be brutally honest the standard "fantasy" version of magic very much has it's roots in lore along with all of the religion and ritualism. Stories about people lighting fires at a whim, commanding the weather, levitating and flying, moving objects, deflecting objects, etc... have existed all over the world, oftentimes without much in the way of a nessicary entity of evocation behind it. This is a point made by a lot of people who do paranormal research in real life. As nerds we like to increasingly draw a line between psionics and "magic" but as far as belief and superstition went, that's a fairly recent distinction. This is to say nothing of things like alchemy. In the real world most of this stuff was tricks, and you can see stage magicians do a lot of the same stuff for shows nowadays, and how some of these tricks have been done (there are various methods) have been exposed over the years. The point being though that in fantasy we're saying there was no trick involved, and that the guys doing this stuff have real powers. It should also be noted that the idea of power being attached to bloodlines is also an old one, albiet in certain cases that can blur the disctinction between magic and faith beause it comes with claims of distant divine lineage. The idea that a Pharoah carries a divine bloodline for example, and that his power is passed down to his male heirs. Such was the logic behind inbreeding to preserve certain bloodlines. The biggest real world example I can think of this happening now was Kim Jong Il (Kim Jong Un's father) who claimed he could control the weather, he and his son pretty much claiming to be bona fide demi-gods.
At any rate, the thing is that in fantasy games once you are acknowleging that this stuff is out there, the rest of it follows more or less naturally. If it's a skill/knowlege you'd expect people to treat it a lot like a profession, get together to form mage guilds, and similar things like you see in most high fantasy worlds. We've even seen it IRL among people claiming to have powers, forming covens, communes, and cabals. Aleister Crowley's "Golden Dawn" and Hitler's "Brotherhood Of Thul" being two modern examples, on a pseudo-religious front we have Scientology (which is about applied knowlege, replacing a "god" with alien space ghosts holding back our potential), and groups like now defunct "Solar Temple" and "Church Of Claire Prophet" The thing is that in fantasy if these guys really have powers and are thus not shy about using them, such organizations are going to be a lot more than just the power of their lawyers, bank accounts, and the number of criminally prone psychos with guns they can claim as members.
On the bloodline aspect of things, a number of fantasy worlds tie magic specifically to that. In many cases the idea being that some slutty deities wound up with mortal progeny who in turn had kids, and thus the gene circulated allowing some people to use magic depending on how active it was for them. Even in cases where it's tied to a specific blood lineage, all it takes is for a few uncontrolled generations of royal bastards and you could wind up with thousands or tens of thousands of magic users within a couple of centuries.
The biggest problem with magic in fantasy usually is when it's a fantasy game. In books it's possible to make magic rare and special by focusing on a handfull of characters and having the rest of the world play straight for them, and having their adventures stand out. In a gaming enviroment though where the idea is for the players to be heroes (as opposed to the uncool crowd that happen to be stuck in the prescence of cooler people) it creates an issue because you usually wind up with multiple people all equivilent to a book protaganist walking around together, requiring extreme threat levels to be an adequete challenge. Even if magic is rare in the world, the nature of a game pretty much means that tons of it is going to be thrown at the player characters (either PnP or in a video game) non-stop. Even if like one in every couple hundred thousand people is supposed to be capable of magic, and only one out of every hundred of them manages to be trained, to keep things challenging pretty much every band of brigands that shows up is going to
have a mage or two with them.
The idea of spell points and such is again gamability in action, when your doing a game you want to get the players to be fairly careful with their resources as opposed to simply doing the most powerful thing possible again and again. Without some kind of measure of fatigue, energy, or whatever, you rapidly wind up with "Captain Marvel" as opposed to a fantasy wizard. That is to say that "Captain Marvel" is magical but he wanders around with all of his stuff going constnatly and uses it "at will" without limitation. Being pretty much a giant collection of "always active" stat increasing spells, flight, and lightning powers, conveyed by a duration free spell, as opposed to a situation where in a fantasy novel a wizard is supposed to do a bit of magic here and there, and be capable of incredible things, but doesn't nessicarly do his "drop meteor on enemy" spell every time he runs into a mugger.
The point here being that when you follow the logic chain you wind up back in pretty much the same place.
I'll also say that one of the very earliest distinctions in fantasy gaming was between "Clerics" and "Mages" to diffentiate the two. Clerics being the ones who use invocations and have magic work through them, where Mages are the ones who know alchemal type formulas, or have "knacks" of their own. While there was early on a distinction in games (for purposes of teamwork) between support vs. offense, that decayed long ago. Even in D&D you saw Clerics and Mages being able to do what the other side normally did with the right spells/builds/kits/specialties as early as 2E. It wasn't all that horrorific though because unlike "Lovecraftian" horror, for every evil, entropy-obssessed demon, or alien entity out to wreck reality, there was some good god of equal or superior power opposing them... with the ensueing celestrial slapfights being the cause of all the crap that spills onto the mortal planes which adventurers have to clean up.
Some world do a better job setting up their magic systems, backround, cosmology, etc... than others. Games and game worlds have come and gone in VAST quantities though because a lot of them don't stand up.
That said, fantasy, even dark fantasy and horror, isn't for everyone. If you don't like magic, there have always been some games on the fringes like Palladium's "Ninjas and Superspies", TSR's "Top Secret S.I." (not sure if it ever got re-done after the WoTC buy out), or even "Mercenaries, Spies, and Private Eyes" which famously inspired "Wasteland".