The US already has a 'loan forgiveness program' that works for every single loan _other_ than student loans, called "bankruptcy". It's worked for hundreds of years, and we used to allow it for college loans.
There is one difference: student loans that are being "forgiven" are being put to taxpayers, whereas in bankruptcy the loans are absorbed by banks that lent money (and to a lesser extent, to parties with outstanding debts, such as vendors).