The value provided by the government is merely the sum of all taxes paid - overhead/waste/corruption. Some people (the rich) get less back than they put in, some (the poor) get back more than they put in. So anyone who is sufficiently rich (1) has probably already repaid any debt they owed to society, and can legitimately secede.
(1) I ignore for the moment people who got rich from rent seeking, e.g. defense contractors, trial lawyers or members of public sector unions.
The problem with going whole-hog anarchism is that on any significant scale (even a couple hundred people) peer-to-peer trust breaks down and anything that steps in to make processes more streamlined and reliable or introduces organizational structure becomes functionally equivalent to a government. We rely to such a huge extent on specialization of labor and trust of abstractions that such freedom doesn't scale if one expects modern amenities.