[throwawaymath]

In the aggregate, yes - given the premise that most potential Feynmans are actually underutilized in society because they can't be reliably selected for. Then I think such a system could arguably be a net benefit, with a greater number of non-obvious Feynmans being selected. The very obvious Feynmans will likely be unperturbed by a lottery because the lottery is (hypothetically) per-school, and they have opportunities to shine in whichever school they join.