My son taught HS because he thought he could make a difference. He probably did, but you can't fight the system. A PhD and teaching again at the college level suits him better, but you can tell he's burning out on teaching, and this last year hasn't helped.
The public school issue probably is a lot less a local that you would hope. Policies come from on high - like ivy league pie in the sky liberal crap from on high. Stuff that's adopted by government policy and forced down the pipe - he who has the gold makes the rules kind of thing. University schools of education are full of the nonsense being pushed into public schools. Once you accept the thought that buying into and understanding the theory of teaching is more important than mastery of the subject taught there's little hope of kids getting what they need particularly in math and sciences. They are going to get what the "more educated" liberals shove down from ivy towers of liberal thought.