When lenders get more stringent about handing out hundreds of thousands of dollars to teenagers, colleges will automatically have to scale back fees in order to get people to apply. No more 5-star hotel rates for shoebox dorms and cafeteria food. No more multi-million dollar pay packages for administrators and sports coaches. No more textbooks which cost $300 per class and need to be "refreshed" every year to prevent reuse. Prioritize lending for degrees which have a higher earning potential and so a higher chance of paying back. Favor students with a better academic record. Enforce a minimum GPA in order to keep getting funded. Issuing loans is a business, so treat it like a business rather than a social service with privatized gains and public losses.
Conversely, the worst thing you can do for the problem is forgive existing loans. What do you then do when universities jack up tuition even more and students run up a tab of another trillion dollars over the next decade and refuse to pay, knowing that the government will bail them out anyways?