Compensated at the expense of whom though?

The taxpayers? Sure, there's an argument for reparations and pumping money into forcing systemic change.

College students competing for a limited number of slots to schools? I'm less convinced of this, it's a zero-sum game where if you're admitting one person you're denying others from that slot.

IMO there's probably better ways you could incentivize colleges to aim for a diverse student body that would be more equitable. The goal should equality of opportunity, not equality of outcomes.