I do think you should be able to declare bankruptcy on worthless degrees. Banks (note that I have a problem with government loan subsidies) should face the risk and not loan to a student getting a worthless degree.
What I can't figure out is how to stop someone who gets a useful degree from declaring bankruptcy right after graduating and then getting a job using that degree. This is fraud.
You never really know when the market would be saturated with degree x since it takes 4 years to earn. On the other end banks may decline a degree that if taken now will start to be high demand when the candidate graduates.
If you have a electrical engineering degree in generators right before someone discovers a cheap over unity solar panel (coming up with a way to violate the laws of physics is left as an exercise to the reader) thus making all generator specialists valueless - most of your EE course work still applies so you just need pivot a little. Maybe you need an additional year of school to get in demand skills, but the odds that you can't find something that it is a low risk to get you into is low.
If you have a degree in music - we already know that field is saturated. If you studied only music you have a few years left to get a course of study that is useful.
What I can't figure out is how to stop someone who gets a useful degree from declaring bankruptcy right after graduating and then getting a job using that degree. This is fraud.