92% of student loan debt is publicly owned through the Department of Education. This department can - and periodically does - write off loans as bad debt for a variety of reasons. And the policies used to determine when the department writes of the loan are set by the department itself.
However, the funding for new loans is derived in large part from the repayment of old debt. So the DoEd could scratch it’s trillion dollar balance off, but would then have this massive liability to the US Treasury with no way to pay it back (not unlike a bunch of the failed private banks during the 2008 crash). And, of course, no new loans would be forthcoming, forcing borrowers into the private lending market (where rates get into the double digits).
There are legalistic end runs Congress or the Treasury could do to avert this. But Dems blocked debt relief in 2009 and then again in 2017. The GOP is openly hostile to any kind of student debt relief, so they’re no help. And the Treasury is just independent enough to tell DoEd to piss up a rope, while backchanneling aid to Silicon Valley Bank and other failed private lenders.
So, it’s complicated. But also, it’s only not possible because we choose to exclusively bail out the Tech/Auto/Finance/Real Estate sectors and leave Education high and dry.