The answer seems to be that the armed band should prefer non-violent means because no one will be willing to deal with them otherwise. I doubt the armed bands are going to care about that. They can steal food, weapons, cars, planes, and any other property they need. Obviously the people who would engage in this kind of activity would reason that they have far more to gain from it than legitimate enterprise, which places some limitation on their power/prosperity.
You need only pay your protection agency contract! The problem with for-profit protection agencies would be the fact that their goal is not protection at all but profit. Their incentive is to offer the least service they can possibly get people to pay for. Top notch protection service sure would be expensive, presumably so expensive that a lot of people couldn't afford it, enabling the armed bands to selectively pick them off. With those groups continually gaining strength in their quest for prosperity and power, it seems to me there would be an ever-escalating war.
Perhaps the response will be "That's not happening today, with state-controlled protection agencies, so why would it happen in the absence of the state?" Presumably people in one city or state or region would have no reason to care about what's happening in any other place, since they have no economic incentive to care, which drastically reduces the threat of counter force in a stateless society. In the present, marauding bands could easily overpower the protective forces in some cities, but if it actually happened the state or federal government--without any profits to worry about--would just call up their vast resources from elsewhere to eliminate the problem. The threat of such significant power promises certain defeat in the present; it would be a hopeless endeavor, and that's why no one dares to try.
