Private armies have a simple problem:
Much like the mercenary forces of early modern Europe, they have the means to take what they want. And their leaders have every reason to keep the rank and file happy, and less so to keep the people happy. The "Captain" or "Colonel" of whatever mercenary company isn't going to take shit from some random semi-armed civilian, milita or not.
Assume for a moment that a private military force has roughly equivalent arms to the US army. That means a civilian militia with shoulder arms, and perhaps a smattering of light artillery would be facing an organized force that has tanks, heavy artillery, body armor, and possibly even airpower. In other words, you could go down fighting, but it would be in their interests to fucking obliterate you, in order to teach any other groups of people not to screw with you, and to pay up when you ask. Basically a protection racket, but with heavier weapons.
Thus, we get looting, rape, and murder. And not in that order, usually.
Aracho-Capitalism suffers from the same problem that Communism suffers from. It doesn't take enough into account how much of bastards people can be to other people.