"Wow, exactly the opposite of the direction that schooling should be moving."
But some won't take no for an answer. They're SO anti-social they'd rather live completely apart than integrate. If forced upon them, they'll push back tooth and nail. But since they were BORN there, you can't just exile them, so you have born-here malcontents who hate you simply because. Haters gonna hate. How do you solve that?
"I'm also of the belief that there should be no private schools."
But that will also be impossible to enforce. Not only do you have the above who'd rather pull their children out of school and enforce their parental duties to the death, but you also have to deal with specialty and trade schools that pretty much HAVE to be privately run because anything else would be hopelessly inefficient.
"Perhaps if Corporate and Wealth taxes were increased and Government incompetence/corruption was great decreased the schools for us plebs could be made to be much better."
Corporate taxes will never work because they'll just pass the costs on. As for corruption, that became intractable with the rise of transnational corporations who can play sovereignty against you ("Shame if I decided to just up and move...").