Adam Smith on who colleges and universities ACTUALLY benefit
The discipline of colleges and universities is in general contrived, not for the benefit of the students, but for the interest, or more properly speaking, for the ease of the masters. Its object is, in all cases, to maintain the authority of the master, and whether he neglects or performs his duty, to oblige the students in all cases to behave to him as if he performed it with the greatest diligence and ability. It seems to presume perfect wisdom and virtue in the one order, and the greatest weakness and folly in the other. Where the masters, however, really perform their duty, there are no examples, I believe, that the greater part of the students ever neglect theirs. No discipline is ever requisite to force attendance upon lectures which are really worth the attending, as is well known wherever any such lectures are given.
Smith believes that in teaching, as in all professions, people work hardest and best when they are rewarded for working hard and well. He also believes that, as with in professions, competition between teachers for customers (students or their parents) will encourage teachers to improve their teaching.

Public endowments reduce the necessity of relying upon fees paid by students to teachers. This reduces teachers’ motivation to work hard to earn their pay or to teach better to avoid losing students to their competitors. Teachers who receive all of their income in the form of a salary will feel the cost of having to work when they teach but will not receive the benefit of increased income from more and better teaching.

Things get even worse when universities force their students to study under certain teachers or forbid them from studying outside of the university. (Smith grants that it’s reasonable to force young boys to attend class.) Forcing students to attend the lectures of particular professors reduces further the motivation to provide value for students by further reducing the competition that professors face for students’ time.

When professors earn their incomes from a salary paid by the public and are guaranteed students by their schools, professors’ positions in the university are more secure but the education offered to students suffers.

Public endowments therefore, by divorcing professors and institutions from the monetary incentives to perform well for students, allow the people who teach in and manage educational institutions to support their own comfort rather than improve the services they provide.

This doesn’t mean that Smith believes that when the public pays teachers’ salaries there are never good teachers. Reputation still matters and good teachers won’t enjoy teaching poorly. But the poor financial incentives may mean that some teachers who could offer excellent education with the right motivation might instead pursue their own comfort and ease without consideration for their students.