In the end, graduates are going to pay for it. But I wouldn't necessarily tie the university with its graduates. What if somebody drops-off? What if, in the future, students will be able to combine classes (and get credits) from 3 universities via online lessons? Each uni can have different system of student debt.

I think, paying per class or year (but rather class) and having student debt as a separate instrument (that can be private or public), is much better.