A "bar exam" for teachers is not the answer. The real answer is to let school administrators from big schools offer better pay to good teachers from smaller schools. After all, that's how we run sports teams. Bring up the good players from the minor leagues. The manager of a baseball team doesn't need to have potential hires pass a test. He's already seen their performance on a smaller scale. By the same token, a competent school administrator will hire those teachers who show good performance on a smaller scale.
How will the school administrator recognize good performance? In a really free society, where parents can send their children to whichever school they want, it will soon be apparent which teachers attract students and satisfy parents.
What makes you think that "big" schools deserve better teachers than do "smaller" schools?
Believe me, America's hellhole cities are not the "major leagues" -- in any category other than the hubris of the imbeciles who choose to remain there.