I'm on the same page with you here. Keep in mind that *states* generally have compulsory attendance (and the compulsory adoption of school districts) in their state constitutions.
I see that as being within the rights of states, and an expression of state sovereignity. If people don't want to live in a high-tax state, they're free to move to a low-tax state.
I'm also with you that private schools in general should be unregulated, but we do have to deal with the question of militant Islamic schools teaching jihad. That wasn't an issue 20 years ago when many of these private school / homeschooling issues were being hammered out.
Or it might be better if we examined our immigration policies so that only those compatible with our values and rule by the Constitution (versus Koran) be allowed to immigrate here. We don't need those who have no use for our values in the first place --- why allow the free-for-all immigration and then attempt to control them in ways that wouldn't be aligned with the Constitution?