Even granting for the sake of argument*, both of Klein’s premises, viz., that university professors do not care about teaching, and that universities are structured not to reward good teaching, this proposal strikes me as a bad idea.  It’s not that it’s unfair; it’s that student evaluations reflect not the quality of instruction, but factors such as easy grading, and whether the professor is attractive.

Providing a handsome reward for good student evaluations isn’t going to give professors an incentive to care about teaching; it’s going to give them an incentive to care about whether they get good student evaluations.   There is not necessarily a lot of overlap. See:  NCLB, call center metrics, etc.

*I’d agree with the second, but not the first.  Plenty of professors care about teaching and do a good job; it’s just that it won’t matter a hill of beans when it comes time for tenure evaluations.