Why? It is perfectly fair for a taxpayer to question public spending, including for salaries. It is when we stop questioning, or start making statements that we should not question something, that we end up with a situation that spending go out of whack since there is no oversight. BTW, that is exactly what happens in the case of CEO compensations also.
Secondly, regarding $150K+ salaries for teachers, how do these salaries compare to the salaries of fresh Asst. and Associate Profs at Universities. Many of them are paid lower I believe, for example Assistant Prof. at UC Berkeley seems to make about $100K [0]. So, there needs to be some oversight around teacher salaries also to make sure that the salaries are actually going to well educated competent teachers and not the ones with some random degree from the University of Phoenix or similar. Education and experience in teachers should be rewarded and the salaries should not be flattened.
EDIT: To add, there are student evaluations for Profs at all Universities. Where are the student/parent evaluations of public school teachers? How are they graded? How are they promoted? Assessment results? If so that is not the correct method, since IMHO it depends more on the parents than it does on teachers. I'll hypothesize, put a bad teacher from a crappy school district in a currently great school district and I guarantee the scores will not change much, if at all.
[0] https://www.glassdoor.com/Salaries/uc-berkeley-associate-pro...