That's the tension between private benefits and appropriable externalities at the heart of state funding for higher education: done properly, it equips graduates to live more productive lives and get richer, but that's a regressive transfer. Read on, though, and contemplate the various market tests.
Let me see if I understand this. Good students pay attention to the academic standing of the institutions they apply to. Good students follow good professors. Good professors can prepare the next cohort of researchers. And good universities compete for good professors.
Sounds to me like a game any university could play, if it wanted to be good.