I think the conventional wisdom is that prestige allows schools to attract better students and professors, and to raise more money from alumni sort of creating

I think the conventional wisdom is that prestige allows schools to attract better students and professors, and to raise more money from alumni sort of creating a virtuous cycle...but to a certain extent its zero sum, so some schools actually end up trying to compete in races that they can't win to their detriment, and effectively to the detriment of their students.