I think that, "what happens if nobody has a standing army?" is an interesting question. What I don't understand is why you think that "someone has to play cop"...?
Or someone gets the bright idea of putting together an army and conquering their neighbors (who don't have a standing army and are relying on Mercenaries who keep a good feel on which way the wind is blowing (and who will have the money to pay them in the future)).
The neighbors, not being stupid, notice this and build their own standing armies (or at least conscript militias). Which is why historically, the situation where there are no armies or militias is so rare: it's not a Nash equilibrium.
