Or teachers are rewarded by educating students, and don't look at it from a totally mercenary perspective.

Which is generally what you want from teachers who ideally can be a students champion, guide, educator all at once, for a short span of time.

Once you tell someone their performance is only correlated with income, then they focus on those levers to manage it.

And once you have a sufficiently complex role, such an incentive structure ceases to be useful, and ends up killing creativity and open minded ness.