All it will do is encourage more borrowing in the hope that there will be another future round of forgiveness. And lenders will have every incentive to offer those loans in the hope that the government pays for it. This money will enable colleges to raise tuitions more, and we get the same problem we've had, just grown more.
Instead allow student loans to be disengaged in bankruptcy. Just like other debts, and just like student loans could before George "W" Bush changed the laws. Now students aren't incentivized to hope for another forgiveness round, lenders aren't either, and we aren't pouring fuel on rising tuition. Plus we'd offer ongoing assistance to those who got in the worst binds. (Unpleasant assistance to be sure. But not a one time bandaid, and very precisely targeted at those who need it most.)