The problem with this is that a lot of students from disadvantaged minorities don't get the same opportunities growing up. They might be just as capable as non-disadvantaged students, but get worse grades because they had to work after school to help pay the bills, or didn't have internet access at home, or a variety of other reasons.
This is why in some systems, there is a different entry stream for minorities. It's been a while since I applied to university, but I believe that in New Zealand for subjects that have a grade cutoff for entry, Maori (indigenous) students have a lower cutoff for entry to account for this.
Of course, this is a blunt instrument in affirmative action. There are plenty of Maori kids who grew up in a middle class environment who are no worse off than white kids, but still get the same affirmative action as poor Maori kids, and there's white people who get left out because they grew up in a disadvantaged environment.
If you could come up with a model that works better than just bluntly delineating by race, that would be great. But it's hard to factor for every variable. Maybe you could base it on the median income for the zipcode of the school that the student went to, but then you'll be fooled by creative accounting and wealthy families sending their kids to poor schools.