The conclusion is simple, not everybody will give a shit about the rules(things like the NAP) in an anarchist society, people will steal, establish power hierarchies, and suppress the new start ups, defeating the very point of a free market. I said this earlier to another person, and I seriously though you'd be able to draw this conclusion yourself. As for the premise, history. Anarchy existed at one point, they got absolutely destroyed by a superiour and more united force.
Consider this, if you will:
Do crime exist? the answer is yes btw
Does everybody follow the law? Answer is No.
If you sign a NAP will everybody follow it?
Will people respect the "rules" and not establish their own state like structure?
Will people accept their anarchist society and not attempt to establish their own hierarchy? Well, ISIS exists, and they sure didn't give a shit about the states they took over, so would they not attempt the same, in a less organized society? They struck oil didn't they? So what is stopping them from hiring more PMCs to establish their caliphate if they were lucky enough to be in an ancap society? Nothing.
Ancap societies has, and is always destined to fail.
Amazing that I have to spoon feed you this stuff.