In a word: No.

Biden has a bunch of scolds cheering this onward, and there are plenty of people who think it would be "popular."

If you're one of them then you're arguing against your own interest for political purposes, and that's dumb.

Broadly the problem with college education cost today is two-fold:

• It's too expensive.  Its expensive because the government subsidized it and removed risk computation in lending.  This in turn made an effectively unlimited price payable by the "student", even though said student had no income, no assets and no guarantee of ever being able to earn enough to both live in a reasonable fashion and make the debt service.  This never happens in a free market because those who lend money in such a stupid fashion lose it when it can't be repaid.
  
  
• Colleges do not care if they sell effectively-worthless educations.  A college would care if it had to underwrite the loans and they were dischargeable in bankruptcy.  If the only actual post-college market for a "gender studies" degree is teaching gender studies then (1) the price will be something that can be paid by someone teaching gender studies and (2) you won't get a loan except on risk-adjusted terms that reflect that.

If you want to solve the problem, in other words, the price has to come down and the lender has to take the risk of default and non-payment.

Thus you do the following:

• College debt from this day forward is dischargeable in bankruptcy.  Period.  It's unsecured debt -- sort of.
  
  
• If your college debt is discharged your degree is void.  That's the hook to prevent "strategic" defaults, which was what goaded Congress into restricting defaults in the first place -- a bunch of high-fautin people who decided to strategically default and eat the 7-year credit ding.  Since there is no physical thing you can repossess but the degree has value and is what was bought then the correct answer is you revoke every credit-hour earned and thus the degree is revoked if a person files for bankruptcy and successfully throws off the debt.  Congress can do this since Congress explicitly has the power to set uniform national bankruptcy law binding in all 50 states.
  
  
• The Federal Government gets entirely out of the college financing business.  If colleges want to underwrite and carry the paper they can, at whatever price they want.  Ditto for private lenders.  The above two checks and balances will make very certain that nobody lends more than can, on a risk-adjusted basis across the pool of students, be paid and thus the price of the education will reflect the actual value in the marketplace.

That's it.  Three simple steps, problem solved.

#1 and #2 are opt in for all current student debt.  This is entirely legal as well and shuts up the whiners.  If you have a "worthless degree" then fine -- turn it in, file bankruptcy, take the credit hit and go on with your life.  When the price falls (and it will, like a stone) and you want to go get it again, have at it, this time at a more-reasonable cost.  No, you don't get credit for the other classes; you said they weren't worth the money so they don't count.  That was your decision, so make if that is your call for both good and bad.

If you simply want a FREE degree, on the other hand, and many people are arguing for exactly that -- the right to steal the cost from other people -- then this change will expose those who have as their actual intent grifting rather than truly being in trouble while making certain those who were in fact misled as young adults have a reasonable path forward.

Fix the problem instead of screwing other people.