The research on this is quite clear:
Charter schools do no better than public schools, and often worse. This is despite the fact that in many places they get their pick of students.
For those who blindly believe that business is always better than nonprofits or governments, that doesn’t really hold up, either. There’s a classic principle: “you get what you measure.” If you measure profitability, then that is what you maximize. For-profit universities have failed massively for just this reason. For-profit grade schools have no reason to do better.