While there are unincorporated areas in the US, I'm not sure no property taxes are a given even in those areas. I live in an incorporated town and definitely pay property taxes and get a variety of town services but do need to handle my own sewer and trash (though I get water and electricity along with fire/police/etc. services as well as public schools as relevant).

In fact, I'm not sure the degree to which just bowing out of public schooling is even allowed given that I think that's over half of my town's budget.