This is a major flaw of AnCap & NAP as a potential system. Until the human nature of people trying to dodge the rules at others expense is dealt with, a voluntary society will just fall apart into chaos and guess what shows up in the wake....... The State.
That's a problem that would quickly solve itself. Those not being responsible with their lives (such as not buying insurance, not taking care of their health, and not saving money for retirement and emergencies) will very quickly find themselves as horrible cautionary examples for others, since there won't be a nanny state to take care of them. And those who are dodging the rules at other's expense will be quickly forced to pay for those expenses, since there won't be a complex lengthy legal thing to fight through, and those who do take responsibility for whom they associate with will avoid you.