There's an even better side effect of this. There is no real and inherent reason that university prices have skyrocketed out of control. It's mostly a consequence of government removing all economic concerns for students. That of course sounds nice, but they also simultaneously removed all economic concerns from universities who can, and do, charge arbitrarily large sums and justify it by increasingly reckless spending. This a recurring problem when messing with the market - we create unforeseen problems, though in this case this should have been very foreseeable!
By returning to market forces universities would be obligated to themselves also take economic matters into consideration with their decisions. Too high of tuition and fees are unlikely to get paid off, thus unlikely to produce much in the way of loans, and thus generally not economically viable. Similarly there would be less of an incentive to grow programs that do not substantially improve the ability of students to create a comfortable life for themselves.
Basically we would start on a path back towards the world some baby boomers seem to think we still live in where somebody with a bit of hard work could put themselves through college with a part time job graduating not only debt free but with a enough of a nest egg put aside to have a nice down payment for their first place.
And if, like now, the government backed the loans and they were dischargeable, it would create a death spiral of companies encouraging loans to no end with tons of students accepting them, knowing that they can just file bankruptcy right after graduating.