I was never too fond of Ilvermorny, I felt as though having just one School of Magic was far too simple for a country as huge and diverse as the U.S. I don't mean that in a SJW-ish way, I know that you all saw the arguments on tumblr, etc etc etc.
I mean that the population of the U.K. in 2013 was 64.1 million, versus 318.9 million or so in the U.S.
Likewise, I don't really enjoy bitching about identity politics, but I do think that the critics had a point about squishing all of the different Native American mythologies together. I actually believe that it makes a lot of sense, but only as a more modern institution.
Chances are, if we're going to consider that Wizards can be just as racist as Muggles, it makes more sense for an Ilvermorny-esque school to exist in Oklahoma, rather than Massachusetts. The Trail of Tears and all that nice business. I love JKR but she kind of dropped the ball on that one.
I'd personally speculate that for the early history of the United States, pretty much every different Native American tribe had its own strain of magic in the same approximate category of "shamanism" or whatever. Wands were an Old World concept that was brought over by boat.
Remember, the U.S. is fucking huge. The population of the country is massive, there's no fucking way that you'd be able to squeeze the modern youth of America into a school like Ilvermorny, even with expansions. Shuttling students over from Florida, Texas, Alaska, and California would be a pain in the ass, even if they did have magical railroads or portkeys or hyperspeed broomsticks. Yeah.
There would definitely be a regal Ivy League-esque school in Massachusetts. Its architecture would remind you of a castle, but it might also be more urban than Hogwarts. A massive school in Boston, hidden in plain sight. How cool would that be? This is the school that is most likely to borrow the Four-House system from Hogwarts. The fancier the school is, the more likely that it's going to rip off Hogwarts, Beauxbatons, or Durmstrang.
After enough generations of immigration, you'd end up with some really funky melting pot wizard culture. Yeah, squeezing all the U.S. magic kids into one school seems like a good idea now, but could you imagine that going down in the early 1900s? Imagine the culture shock.
I'd imagine that in pretty much every historical U.S. economic center would end up with their own school, one that both urban and rural students could make the journey to. Could you imagine the sports teams? We missed out on so much. I bet that American Wizards would have their own sport they'd be crazy about, like American Football for Muggles. I want rabid American magic football fans.