It's a shame that we're here in 2021 and the best we can do is basically just "selection bias." Basically all universities have no statistical proof that they can educate people beyond this. This is not to say that the schools are bad, but most of the education is simply due to the types of peers you have, not really due to the school itself. Princeton and Harvard admit, for the most part, people who already excelled…
Princeton spends roughly $270,000 per student (see footnote). I'm sure some of that goes into research as well, but it's a relatively small fraction, since Princeton prides itself as being a teaching university. I suspect that you can build a more successful university by paying students $100,000 a year, hiring grad students to teach, and paying for modest facilities.
(742,123,000/.33)/ 8,374 = 268552 https://profile.princeton.edu/finances https://en.wikipedia.org/wiki/Princeton_University