It will take more than a couple of generations, because the children of people who got legacy admittance also get legacy admittance, which removes available slots for people who don't just have the benefit of being born to the right parents.

That's the big cudgel right: look at the racial spread of legacy acceptances, and if that does not match (within reason) the average racial spread then legacy admittance is adding a discriminatory pressure against those races that are less represented.