Once we pay anything to these debts, we will always pay for them. People go to college every day, a one time payment today will not help the debts of tomorrow. The debts of tomorrow will say "they got their debt paid, I want mine done too."
I am also willing to bet, even with the rising tuition rates, if we start paying, those rates will rise at a higher rate than they are now.
It also does absolutely nothing for the immediate future, which is what we need to pay attention to. Suspending payments? Yes! That is fine, but debt erasure has greater consequences than are worth it for getting the economy moving again.