See the other comment:

Banks will lend less, to people they think will pay it back. Which means schools will have to charge less, particularly for non-profitable majors.

The govnement is the creditor, not the banks like they would be for a traditional loan.

Hmm, I didn't realize that federal loans were the overwhelming majority of the student loans (I guess the pseudo-governmental status of Sallie Mae and getting federal loans serviced by banks was a bit confusing). That does complicate matters, and suggests that universities are enjoying the government guarantee of funding to increase costs. Making them dischargeable in bankruptcy would mean the programs would have to change.