Are Ivy League schools overrated?

(That said I agree with your premise, my peers at school aren't significantly more intelligent than my high school classmates who went to good, but not great, private and state colleges).

What ivy league and other private research universities excel at academically is scholarly opportunities outside class assignments. If you want to reconstruct 17th century pipe organs or build robotic insects or experiment on extremophiles in Greenland or whatever, there might very well be someone who wants a student to help with something like that. Plus they probably have money to cover your expenses and pay you a stipend for it, and you don't have to compete with 500 other people for the chance. More generally, if there is a particular academic topic you as a student want to learn all about, a top university has a better chance than most places of having someone or something that can help you. But the student has to show up with the initiative and persistence to get that.

The hard part is admissions: what's the best way to find students who will of their own volition seek this kind of thing out? The simple answer would seem to be to look for kids who have a history of doing that and succeeding. But instead that produced this arms race of people seeking lots of extra academic experiences purely for the sake of getting into college and then burning out and not wanting to continue once they got there.

This is actually true at any school. At large state schools, there are professors doing real research. The difference with the ivy leagues is very few students actually seek these experiences out. (I was one of four undergrads applying for a paid research position during my Big School CS undergrad. I got it as a sophomore because the competition was weak.) I still would have had a better experience at Stanford or MIT, but I think it's more a peer effect.

But instead that produced this arms race of people seeking lots of extra academic experiences purely for the sake of getting into college and then burning out and not wanting to continue once they got there.

This is very true. I was very surprised how many of my friends dropped their extracurriculars in college. The only friends who stayed in music were the ones (like me) who went to large state schools - in essence because we were doing it for it's own sake. Turning college admissions into an extracurricular quest (in addition to a "Don't dare get a B" risk aversion) seems very wrong.

My sense is that this gets sorted out in the end. After a few years of work, all the nonsense about school admissions is gone.

Indeed. Once you factor in the athletes and worse, legacy admits, Ivies have real trouble building an all around good class by the metrics most in this discussion are using (by their metrics, they're education the future leaders of the US and world, so...).

MIT and no doubt CalTech have a great advantage in that the first calculation in admissions is "can they do the work?"; that, which is a rather high bar, plus tremendous self-selection in applicants, results in a somewhat different student body. Or at least compared to nearby Harvard by my observations.

This is actually true at any school. At large state schools, there are professors doing real research. The difference with the ivy leagues is very few students actually seek these experiences out.

I completely agree (having been at a large state school) that there are many professors doing high quality research at state schools. I think the difference is (as you suggest) the funding and competition. Funding and even for-credit programs for undergraduate research were (I found) much more limited at state schools. You'd have 10 students, all with straight A's, applying for a single one-semester research assistantship that'd grant 1 course credit. At the same time I know of ivy school subject-specific fellowships of thousands of dollars for summer travel/study for which perhaps only 2 or 3 people would apply simply because there were so many other opportunities available. The net result is that if you're at an ivy, that kind of experience is much much easier to get.