There was a time when it was this way. There's a problem with this method, though. What happens (and did happen) is that the classrooms empty out, but not for the reason you think.

First: only rich students get student loans, because poor students are less likely to be able to pay them back, they are discriminated against by lending institutions. You contribute to the problem that education is supposed to help fix.

Second: Middle-class students who are able to get loans do so, pay high prices for school, graduate, pay off the last of their tuition with loan money, then immediately declare bankruptcy the second their feet leave the graduation stage. They have no assets, so the proceedings are very low-cost. They live with the support of their very privileged families (no poor students getting loans in this world, remember) during the 7-year bad-credit window while sacking away every penny, then burst onto the scene with clear credit, a huge nest-egg, and a costs-as-much-as-I-feel-like degree while the banks decide that the sorts of students who want a loan and are smart enough to profit from it are exactly the kinds of students that they don't want to give loans to.

Student loans dry up because you're either too poor to afford it, or too smart to be trusted with it.

Something similar happened during the housing crisis, in which the people with the best credit scores were more likely to default than those with patchy credit scores because they realized that the hit to their credit was less damaging than paying off an underwater loan.

That's why student loans are guaranteed.