One private-sector approach would be to fund education with equity instead of debt. Lenders can agree to fund a student's tuition in exchange for X% of their income for some fixed number of years Y after graduation. The lenders can choose X% and Y, within reasonable limits. After that period expires, no matter how much has been paid, the student has no further obligations.
The average cost of a 4-year undergraduate degree in the United States, including room and board, is around $76k. A lender might agree to pay this in exchange for 20% of wages for 10 years after graduation. The median income for fully-employed people with undergraduate degrees in the United States is $56k per year, so assuming the student earns that the lender gets a total return of $112k, or 47% ROI, over ten years.
That's roughly the same as debt with an interest rate of 4.7% percent, which is similar to what lenders are charging these days. The difference is that this scheme shifts the risk to the lender, where it should be: banks are experts of credit risk assessment.
Since lenders only get paid when the student does, their interests are better aligned. If you graduate and end up making a very high salary, they get a lot of money (and so do you of course); if you can only get minimum wage jobs, the lender doesn't make a profit. So they actually has an incentive to ensure the students earn more money after graduation to maximize their own return. Lenders would probably start competing with each other on job placement programs and whatnot.
It also puts the burden of the cost of education on the lenders, not the students. Lenders here have more bargaining power with schools, so they'd be better able to apply downward pressure on tuition fees.