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.
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?
Also, the labor market for most govt employees is not remotely a free market. Unions keep out the competition, essentially getting no-bid contracts to supply labor. They play politics to elect politicians who will give them what they want - in many cities the teachers unions essentially control the political system. You might as well call Halliburton's no-bid contracts in Iraq a "free market". It's a "free market", closed to new entrants, with no negotiation between the buy and sell side, but with the buy and sell side colluding to rip off the public.
In any case, just because it's tough to quantitatively measure some development does not mean it's tough to measure teacher performance. Students either know the material at the end of the term or they don't, simple as that.
All the whining about how it's impossible is really just an attempt by teachers unions to avoid accountability. I'm sure Halliburton would love to avoid accountability for their performance in Iraq and elsewhere too, doesn't mean we should take them seriously.