And the schools should not be in the business of telling students what they can afford. For one thing, they probably can't know.
Without the government guarantees, banks would think hard about whether a loan was repayable, and schools wouldn't have nearly as many anthropology or art history programs cranking out unemployable specialists year after year.
The government guarantee removes economic consequences for certain actors -- for the school and the bank, but NOT for the student. The student with an art history degree is now stuck with a massive loan that is not even dischargeable in bankruptcy, whereas the bank and the school suffer no consequences for having trained someone in an unemployable specialty of little to no economic value.
On the contrary, they are incentivized to do that.
I'm not sure you're using the term "moral hazard" correctly. If the loans were dischargeable that would be a moral hazard, because the smart thing to do would be to borrow up to your eyeballs and then declare bankruptcy ten years later on graduation day.