if you have been within 50 miles of an ivy you know the kids there tend to trend rich. the parents can afford the school. the parents can send their kids to private schools who produce most of the kids with high SATs. i have never felt so socially out of place as at an ivy.
i say this because when you start throwing around abstract numbers saying, "but x% of kids there don't get aid" or "a lot of kids get little aid" -- it's those rich kids. this is not state college. this is not even your local liberal arts college. this is definitely not penny pinchers at your local juco. roughly 26% of harvard parents make >$250,000.
how they get treated or their affordability is irrelevant to me if i am poor. at a cutoff of $200k harvard is free tuition. at a cutoff of $100k they toss in room, board, and expenses.
if i am below those cutoffs, my issue is not affordability -- IT'S FREE. my issue is getting in. my issue is socially fitting into a school filled with rich prep school kids. and your issue is managing to make the required SAT while going to a public HS. i don't think people get how it works. one inner city HS the average SAT might be 900. down the road the suburban HS is 1150. tucked away nearby is the private school which averages 1400.
it's very simple. which kid is more likely to get the 1500+ you need? a slightly above average private school kid. the kid who does it from a suburban public is a star. and no one ever does it from the inner city school, but we pretend we don't need affirmative action.