There's a reason the federal government is as involved as it is. When I started college, lots of students dropped out because they didn't have the money. My first semester, maybe five students I interacted with dropped out within a few weeks. "Going back home to work. The loan didn't come through." That was back in the old days, when tuition was cheap, before states decided to end support for university education.
The better policy would have two parts:
- A maximum (like 7%) of your after-tax income can go to student loan repayment.
- Colleges have to partially repay loans they took for tuition if after five years the student isn't on track to pay the loan off. This would align the incentives of the college with those of the student. It would bring a fast end to students that borrow to pay $75,000 a year for worthless programs.