I wasn’t arguing for teachers getting paid little. Just pointing out the fact that an increase in teacher pay would result in different people becoming teachers.
Here is a study that shows that content area expertise is the best measure of student achievement https://epaa.asu.edu/ojs/article/view/392.
The existence of charter schools had nothing to do with the simple fact that increasing teacher pay would change the labor supply. But even if that was the case, federal policy mandates that charters either use blind lottery or weighted lotteries that can only improve the odds for economically disadvantaged students. So although cherry picking can happen, there’s very little evidence that charters, as a whole, cherry pick students despite the frequent smear campaigns.