Part of it not said in any of the other answers is that schools are managed at a very local level and get a significant amount of their funding through local taxes. So, you get a lot of towns that don’t have the local tax base to raise revenue or you have a local tax base where the wealthy few would rather pay for private school than the taxes to pay for a better public school.

The problem with organized labor in this case is that the organized labor is generally fighting the government and a lot of states don’t want an effective union network getting built or spreading.