I didn't even think about this through the mid-term viewpoint, but it makes total sense.
The 5-10k is a possibility, but I think the more probable option is extending the current administrative forbearance and interest rate suspension through 2022. That will get the Dems through the elections and really start racking up the numbers for marketing.
"We allowed $500,000,000 (or whatever the hell the number is) in student loan payments to go back to the borrowers/economy. Vote for us!"
Then Biden can screw around for another 12 months, making promises about "looking into" forgiveness, then all of sudden, he's running for President again. (Or Harris is, and he's a full-time fundraiser.)