But the schools are profiting immensely from the difference between the perceived value of a degree and the actual value. They'll never get into the loan business without being forced.
But I agree they should have some skin in the game. My favorite idea on that end is students should be able to partially default on loans, and the schools should be required to share the loss with taxpayers.
A couple of points:
First I don't think such a school would remain the best very long. There was a time when CCNY and the CUNY system in general had a fantastic reputation largely because it served an immigrant population that the Harvards of the world refused to take on as students or faculty. CCNY's fortunes turned around for many reasons, but one of them was that the traditional top schools dropped their racial/ethnic quota systems and introduced aggressive need based scholarships.
Second, I think we a society need to move away from the idea that 18-22+ year olds are still members of their parents' economic unit. In Sweden college tuition is free, yet the percentage of students taking out loans is higher than the US because there is no expectation that parents will pay living costs. Perhaps banning co-signers for such student loans is going too far, but perhaps not.
I don't think the choice is "lend the kids a whole bunch of money to let them in" vs "don't let them in at all."
It's "lend the kids a whole bunch of money" vs "don't lend them a bunch of money, and still let them in."
It's possible I'm wrong about this, but we've definitely went too far in the other direction.
But for the many excellent schools without massive endowments, the risk of letting in more qualified "Caa3" applicants over "Aaa" applicants could make a substantial difference on the margins.