Doesn't it depend what the private universities do with the money? If it's spent on enabling people to attend who otherwise wouldn't be able to, that seems good (regardless of how large the endowment at that university is).
Instead of rationalising, try researching. Ivy League universities, for example, almost uniformly use "need-blind admission". Meaning they admit you first, and the decision comes with a promise to find a way to make it affordable for you to attend given your circumstances.
