But that might be counter to their whole nature. Doesn't mean anyone's being irrational though. They're now de-facto gatekeepers on entering the professional class. I don't think it's unreasonable for the gate-kept to have opinions about the -keepers.
If you're a billion-dollar company that only hires college grads, it feels like there's gotta be value to you in making sure there's more meritocracy in the process of getting degrees.
It would also change who the customer is so that the university doesn't "owe" the student a degree which makes the evaluation that universities do a little less rigorous.
(Companies do subsidize that limited set of schools, and pretty heavily, but it probably has more to do with social connections than economic merit.)
The system might break down to the point that what you're suggesting makes sense. On the other hand, "Indebted Worker" (from any of the three types above) allows companies a lot of power over their employees, so it might not.