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).
As a datapoint, "Fifty-five percent of Harvard College students receive need-based scholarship aid, and the average grant this year is more than $53,000." (https://www.google.com/search?client=safari&rls=en&q=harvard...)