This would make getting a job out of college SO MUCH HARDER. Companies would do everything the could to get existing employees in the workforce, for whom someone else has already paid off their loan.
Much like cell phone carriers locking you into a contract, companies would try to force you to work for them for X number of years because they paid your loans. I suppose this could work similar to vesting, so it wouldn’t be impossible. But companies would still try very hard not to hire anyone with student loans. It would just benefit the wealthy people who don’t need them.