In Deathly Hallows, the Ministry made it mandatory for every wizarding child of school-going age to attend Hogwarts.
I'd forgotten about that; but then again, I formed most of my opinions regarding Potter canon when I was a teenager reading books 3 and 4. I was an adult by the time I got to Deathly Hallows, and I didn't read it too closely.
I suppose Goblet of Fire could be said to imply wizarding schools are fairly rare, though; it never mentions any continental schools besides Durmstrang and Beauxbatons. The movies seem to imply that those are all-male and all-female respectively, which might in turn suggest more schools offscreen, but I don't think the books do.
I could be wrong here, but I definitely remember someone, maybe Hagrid, claiming early on that Hogwarts was, "the best school in magical Britain." That implies others. It's entirely possible that newer magical schools without a history of legendary wizards and a past alliance with two other prestigious schools would go largely unmentioned in the original Harry Potter.
Warning: As per the official spoiler policy, the following discussion may contain unmarked spoilers for up to the current chapter of the Methods of Rationality. Proceed at your own risk.
Assume HPMOR was written by a super-intelligence implementing the CEV of Eliezer Yudkowsky and assorted literary critics. What would it have written differently?
... is what I want to know, but that's hard to answer. So here's an easier question:
In what ways do you think Eliezer's characterisations/world-building/plot-fu are sub-optimal? <optional> How could they be made less sub-optimal? </optional>
(My own ideas are in the comments.)
To put it another way... Assume a group of intrepid fanfic writers in the late 2020s are planning to write a reboot. What parts of Eliezer's story do you think they should tweak?
And just to make sure we're all on the same page: Eliezer isn't going to go back and change anything he's written to bring it in line with anything suggested here. This is purely an "Ah, just consider the possibilities!" thread.
... which means that we can safely suggest drastic rewrites encompassing 30 chapters or something. Or change fundamental facts about the world.
(Exercise due restraint on this one. Getting rid of the Ministry/the Noble Houses/blood purism would probably turn the story into something completely different; this isn't what we're trying to do here.)
With that, let the nit-picking begin!!