Programmers may routinely be judged by peers, but the entire team is then judged by results. A team that can't ship gets the axe or goes under. The closest counter-examples to this I can think of, doing government contracts, have also been some of the worst software shops that I've encountered.
So what's the analogous mechanism going to be? Are you ok closing entire schools if they have lower than average test scores in their class (whatever this means)? Otherwise, how do prevent the whole system from devolving into politics and cronyism?
In almost no city does the teacher's union essentially control the political system. The police union is always, always more powerful, for one. They're just more politically engaged, people who are driven by power. Several private unions will be more powerful. And that's leaving out every power broker that isn't a union (representing most of the power).
"All that whining about how impossible it is to measure programmer productivity is just an attempt by developers to avoid accountability." You might consider that you don't know a single thing about teaching in a non-college or lower-class environment. No offense. I don't claim to, either. But I'll at least listen to what every teacher I've ever met says about the matter.