The old chestnut, 'But wouldn't the warlords take over?'. No, they wouldn't because voluntary agreements with multiple competing security providers would exist, and those providers would have agreements with each other when violent incursion affects each other on a scale that is outside the limits.
Note also that historically, such as the war of independence and the civil war, it was a mix of regular and irregular forces that came to win in the end. This is something that can only happen when anyone with the will to pick up arms and learn how to use them and who makes the effort to be communicative with the more formal, organised forces near them, can produce defensive capability that can repel all but a greatly overwhelming size of force. The bigger the force, the greater the chance that more people from a wider geographical region would get involved.
Capitalism has the advantage that people who adopt it as strictly as in the anarchocapitalist form of it, are both wealthier and more peaceful. It would be extraordinary for an outside force to come into play or even an internal force that does not understand that production and productivity are the key to winning wars, would not be less equipped at waging war. The USA was the main winner of World War 2 not because of anything other than its long period of relative peace and capitalism had provided far more resources and capital in the form of productive capability, that the soldiers had more power per person than either side of the enemy.
The warlords wouldn't take over because they'd be so tightly organized and intertwined with the economic order as to be indistinguishable from a government. ;)