I really like the point you make about randomness being bad as well, albeit in different ways. I’m not sure if I agree on the prior-grade route, not for freshmen at least but that does make a lot of sense for the later years.
Overall, randomness, like democracy, might be the least worst option.
IMO randomness removes accountability. Imagine needing a class to graduate and the gods of the PRNG don't allow you to register in time.
Better to have at least one aspect within your control (e.g. completed credits or GPA). I'd much rather have to go to school for another semester because I'm lazy and drank too much than just getting cursed by bad luck.
Overall, randomness, like democracy, might be the least worst option.