I would be more likely to teach in a private school than a public one, for sure. But I have a different job for now so am not pursuing it. That doesn't negate the point I made (and which a sibling commenter has said also applies to his/her case).

I'm not sure the point of your last comment. Of course everyone wants to be paid fairly for what they accomplish, which is not just based on intelligence, but also hard work. I have done a very good job educating my own children and have seen enough laziness in our public schools that I'm certain I would be more effective than a great many of the teachers.

But more importantly, if the incentives were aligned then even better teachers would enter, perhaps leaving me in the bottom part of the distribution. Nothing would make me happier than if schools were filled with teachers who were so effective!