I think you can reduce inequality through race-neutral policy but you can't eliminate it. There are too many factors that interact with each other to be able to set laws that target all of them without ever addressing the unifying factor that led those inequalities to group in the first place.
While well-intentioned and I'd approve, university is not the source of the most important inequities. High school is more important than university, and elementary school is more important than high school.
Sadly the problem is the same now as it was in 1955. Until the average Black kid can regularly live in the same neighborhoods and go to the same schools as the average White kid, education will not be equal. I'm not talking about forcing Black kids to be tokens in an all-white environment, I mean actual integration. Any system that doesn't involve real integration is going to perpetually have to fight the transfer of crucial resources (not just money but also access to services, positive and healthy physical environments, and human capital) that otherwise will continue flowing from the have-nots to the haves.