Banks are guaranteed payment on the student loans they issue (yes there are exceptions but that’s not the norm). The norm is that either the student pays back the loan, or, the government pays back the loan. That’s why banks have decided to loan out 200k plus loans to 18 year olds. State schools or private schools, it doesn’t matter. If the customer is willing to pay more money for the same product (because loan sizes from banks keep growing), then there is an opportunity to raise prices. Sure costs have gone up for schools over the years, so have expectations for what schools provide (more amenities, more staff, more sports programs, etc). That’s only a fraction of the reason for hire school prices.

If you capped how much banks could loan on guarantee, you’d see prices for schools drop pretty sharp. Mark Cuban has talked about this a bunch over the years.