By this logic, wouldn't it be beneficial to the economy generally to bail out ALL debt? Cancel all mortgages, auto loans, credit card debt, etc. Why wouldn't this be an even better idea?
Indeed it would help those who are in debt. But:
1. The government doesn't control those debts. Various other lenders do. And only the lender can choose to forgive a debt. We're talking about a government policy with the government's own loans here. It can choose this policy for itself, but imposing it on various private lenders is separate issue that's really not within the realm of possibility for this country, or most people's idea of what reasonably should be possible.
2. The government not only has the choice to do this for itself but not to compel other lenders to, but also has a responsibility to "the general welfare" which those other lenders don't share.
3. In at least one of those cases--mortgages--governments have essentially ordered lenders to forgive or partially forgive loans before. The "housing crisis" was caused by people borrowing and then not being able to pay, and part of the response was to require the lenders to let non-payers keep their houses anyway, depending on circumstances. And, although I can't think of a case in which the same kind of thing has happened with auto loans, the fact that auto loans have such a tendency to get borrowers in trouble they can't handle has also led to a common public view of auto loan lenders as criminals at least in essence/spirit if not in technicality, so a lot of people certainly would agree that doing something about those would be good too. Also, consider the fact that a bank deposit is a loan from the depositor to the bank, which means the FDIC's deposit guarantee is essentially a partial forgiveness program for loans/deposits larger than the guarantee's limit. So the concept that loans are a burden that people would be better off without is not at all unthinkable or unprecedented in the world of private business loans, as you seem to think; it's more like an uncontroversial fact.
4. The scale of what the borrowers have borrowed and what they've gotten for those loans is far off. The amount of money that's involved is normally larger than just about any other loan a person can get. And with the other kinds of loan you're talking about, the borrower already got what (s)he borrowed for. Borrow for a vehicle, and you get the vehicle first and start paying later. Buy a can of paint with a credit card, and you get the paint first and pay the credit card balance later. But what gets college graduates in trouble is that they often did not get what they were told they were supposed to get for it. In private loan world, this would be called fraud, which can indeed be a cause for partial or total forgiveness/compensation.
5. The scale is far off, not only in what the borrower gets, but also in what the lender would lose. Most private banks & credit unions & other loan businesses, if the loans they had already paid out were cancelled, would immediately lose more than the value of their entire companies. For the Federal government, on the other hand, the lost income from student loan forgiveness would be like the amount of skin cells you lose by scratching an itch. The total of all student loan balances that are still out from all the loans that have been made over the years is literally a fraction of not just the whole annual Federal budget, or even just the Defense Department's annual budget, but the
increase from one year to the next that the politicians who say we can't afford this keep routinely voting for in the Defense Department's budget. So the harm that would be inflicted by universal private loan forgiveness simply doesn't exist at all in context of Federal student loans.