First, I'm surprised to hear that there's no way to make an unfair process fair, if the system as a whole is unfair. That should put a stop to most social justice movements.
But higher education policy isn't like that at all. Helping the average 18 year-old learn more is a totally valid goal of higher education policy. Helping below-average 18 year-olds learn more is a totally valid goal of higher education policy. If the powers-that-be think it's useful to ability-rank 18 year-olds for pedagogical purposes, then perhaps that's correct. But the second stage of the college sorting process where more resources are expended on a UC Berkeley student than a community college student doesn't have any justification. That unfairness permeates the entire system. And because the system is unfair, there's no way to incorporate race (or not incorporate it) or to replace race with class or geography or anything else that will produce a fair outcome. [Italics mine]
Second, there's a perfectly rational explanation for why resources are spread disproportionately. It's the same reason older colleges and universities tend to have more resources and more prestige: time helps to generate the perception of being better through creating a history of actually being better. The University of Michigan is the highest-ranked college in Michigan because it had more resources, and earlier, which makes it easier and more straightforward to continue giving it resources. After all, starting up a new university is massively resource-intensive (which is why there aren't a lot of new universities), and those resources are generally better used at a place that has demonstrated the ability to use them well. That UC Berkeley is better than a community college is no surprise--it's a historical-institutional matrix working out in a perfectly rational manner.
Third, let's assume the claim, and see what it gets us. If the problem in the system is unfairness in directing disproportionate resources to some small set of people, then there was no more unfair act in any state than the establishment of its first public university: by definition, the state gives unfair advantage to some small proportion of people, and everyone else is excluded from the good; if your first class was four or eight people, as at Michigan, there could be no justifiable way of picking out the worthy. This would mean that the Morrill Land Grant Acts were unjust and unfair, since they did not mandate equal educational outcomes for everyone.
Fourth, it's a remarkably clear example of walking right into the trap Nozick sets in Anarchy, State and Utopia: an educational system cannot be fair unless it is, at every moment, ensuring a fair outcome for everyone. But the only way to do this is through constant and deep intervention, which I would imagine people might find objectionable.