Let me start by saying that this is an interesting idea.
Short answer is no, there is government regulation from some level, no mater how independent a place is.
Having said that, the closest thing to what you’re looking for would be the top excusive gated communities where although they are within a township or municipality, they have little to now reliance on the public system. The community association fees pay much the same as taxes would for the creation and maintenance of streets, services, and utilities and all the residents send their kids to private schools. But then again, even these associations are set up like a government with elections, board members, and they create their own rules and regulations.
Ironically the wealthier a person is the less they need or use public services.


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