Part of schools "affording" the best teachers is not money, but the amount of discipline problems they need to deal with. Which correlates to the financial status of the families at that school. For tons of reasons.

Which families tend to win the lottery to go to these schools? The parents that can afford to. Even if the school is free, the transportation is often not. Plus the parents have to have enough free time to be aware of the lottery for their 3 year old.