Right up until the vagaries of random chance give some individual/group a little bit more power than anyone else, which they use to get even more power and then you end up with these groups running things.
Once achieved, the equilibrium of NAP should be very stable. Reemergence of government in a post-government world is akin to educated people returning to the belief in a flat world that rests on the backs of four giant elephants! How do you get 7+ billion self-interested individuals to stand by while some upstart wannabe enslaves them? In adsense of the "divine right of governments" delusion, this much concentration of power in the private sector is simply absurd.
Free Market Capitalism won't prevent this because it can't, in order to prevent this you need people with perfect knowledge so they react against these vagaries, but people don't have perfect knowledge especially not the hyper individualists you postulate here, since they'll inherently be adverse to sharing knowledge *they* have.
First of all, describing current governments as having "perfect knowledge" of anything is just simply funny. Secondly, this is a case of comparing a closed centralized system with an open polycentric one, like Microsoft vs FLOSS (except Microsoft is less incompetent than the government and is not in a position of being corrupted by total power).
Your claim that individuals will refuse to share knowledge, even when it is in their self-interest to share it, is totally baseless - what will happen is the very opposite. We're already seeing this effect take place in every aspect of the Internet, and it will continue to expand. People post reviews of local restaurants because it makes them feel important, they post their little shell scripts or photos of their cats online to attract attention to their site, they edit Wikipedia to add in missing pieces whose absence bugs them, etc, etc, etc - the same will apply to methods of polycentric surveillance as well. In some cases sharing outdoor security camera feeds and other knowledge will be essential for their safety - and they'll know it.
In a postmodern society you'll inevitably have high-tech eyeballs: like billions of live-streaming cameras everywhere, satellite sensors, buffers in everyone's augmented-reality glasses, hovering / underground / floating pollution tracking bots, etc, etc, etc. For example, guns would likely have built-in cameras (strongly encouraged by neighborhood regulations, liability insurance plans, etc) to document self-defense. Imagine Google Earth, but with everything integrated into it, live and with time-shifting, all coordinated by AI - you can track anyone almost everywhere and anytime. Privacy will become a feature, not an expectation - blind-spots (ex. private residences) will obviously exist, but you'll know who entered them and when. In order to constitute objective evidence (as video/etc from a closed feed can be faked), those data sources would have to be streamed live and be "open source" - one camera is watching another. Polycentric jurisprudence would require property records and some types of contracts to become open public record. Think of it like trying to falsify well-exposed HTTP content history, but with video - you may be able to somehow hack the original site and even Google Cache, but what about Archive.org and Bing and Yahoo and a hundred other scrapers who've observed the content prior to your tampering? Non-contradiction among multiple third-party-owned live-streaming witness devices makes for objective proof.
Technology will eventually make secrets very difficult, and crime as we know it pretty much obsolete. It would be next to impossible to get away with failing to clean up after your dog in a shared neighborhood park, much less build an army! Game Theory 101 - "everybody wants to rule the world", but nobody wants a certain death trying! And who would this madman hire to be in his army? In absence of the recognized "divine right" to tax and print "legal tender", how would s\he pay them? Governments have vast amounts of power, including "soft power" (ex. monopoly on regulating child education, licensing of media, etc) - once that's gone it would be utterly impossible to recreate that much irrational public obedience on a large scale!
In a government-controlled world all this technology would constitute a Big Brother dystopia, but in a decentralized free market and with natural pressures to encourage "open source" interoperability, it would be a fairly innocuous fact of life. The paranoid would move into neighborhoods with strict anticam laws and privacy domes, but that doesn't constitute a threat. Most people will just learn to avoid lying, and mass-psychology will adjust. Anyone who is interested in "evil madmen trying to take over the world" scenarios (and there inevitably will be people who'll be obsessed with these sorts of "conspiracy theories") will have no less "perfect knowledge" than governments have today. Powerful individuals will be under constant scrutiny, with great pressure for transparency and audits on top of audits by independent agencies - if they remain suspicious for long, then their businesses will be ostracized, and their power will deflate considerably. And, hypothetically speaking, if those "evil madmen" were to succeed, the worst they could do to stabilize their power is create the same kind of demagogic "mommy government" systems we have today!
Needless to say, governments will not be phased out overnight, but in the coming decades they will become less and less relevant as technology makes more and more of their functions obviously unnecessary. Who needs borders when the whole world is economically integrated? Who needs roads when you have flying cars with P2P wireless collision avoidance and liftoff/landing coordination protocols? Who needs the FDA when, as you look at a product, your glasses feed you aggregated summary icons from independent labs and QA agencies, which compete with each-other based on their reputation for accuracy and incorruptibility? Who needs a welfare bureaucracy (which currently spends $60k per family to keep them in poverty) when "mandatory direct aid" (a gradualist stopgap solution) and eventually private charity achieve far more cost-efficiency while actually helping people overcome their problems on a personal level?
Freedom will not advance uniformly, but the places that conduct smartest and fastest reforms will attract the top brains and capital, while socialist holdouts will become isolated and backward as they simply run out of competent people to tax. Governments have always relied on their influence of media and exaggerated external threats to strenthen their power, but the Internet levels the playing field a great deal. If they ever have to "send in the tanks" to crush a secession movement, the whole world will be watching the bloodbath on YouTube (or WikiLeaks, or The Pirate Bay, etc), and tyrants will ultimately have to yield to public sympathies to retain whatever shrinking scraps of power they have left.
Congratulations you've replaced regulatory capture with feudalism.
I've "replaced" nothing. I've laid out a vision for the evolution of governance systems in light of future technological and social trends.