Well, obviously it does not make sense to give any kind of scholarship to the children of the very rich, but I don't think that's what "affluent" means to the people who wring their hands over this sort of thing. You really have to be dirt poor to get any kind of grant, as opposed to loan. I grew up in California and I knew a lot of kids who ended up going to UC despite being admitted to elite private schools, because the financial aid powers that be assessed their families for ridiculous sums. The assumption is if you have any money in the bank at all, you have to sacrifice your retirement and the education of your younger children in order to send the child to school. The value of the family home is also taken into account, because they are supposed to take a second mortgage on it. And if your parents are divorced and remarried, the income of the stepparents are taken into account, regardless of how long they've been in the picture, what kind of relationship with them you have, or whether you even live with them.
Basically it is a system of milking the middle class parents of able children to subsidize feel-good charity for affirmative action cases. And the so-called beneficiaries are being hurt as well in the long run, because straight out grants are a drop in the bucket. Most of the financial aid package is loans, and people who have no real prospect of ever earning enough to pay them back are being lured into borrowing 40, 50, 60 thousand dollars for the benefit of the school. It is a good thing for aid to be based on ability, it keeps young people from being lured into debt out of all proportion to their objective earning power. Of course I think a society which requires its young people to mortgage their futures in order to get their foot on the first rung of the ladder, while elderly people who've had decades to save and plan are swimming in government benefits, has its priorities all out of whack, but that is a different topic.