Why not actually? Instead of politicized solutions one could require schools at every level to create some sort of random admission pool for some percentage of yearly admissions.

For instance, take the mean SAT of admitted students, lower it by X% and pick candidates to random pool with scores above that level.

I imagine that to many people it wouldn't be "fair" because it wouldn't bring the outcome they want. But it'd be fun to watch them argue that random system privileges XYZ group!