(In fact, large resources devoted to law enforcement are usually a sign of the state's weakness, not strength. They indicate widespread law-breaking, which in turn indicates that a lot of people are in a position where it seems like they can get away with it -- and the state is, for whatever reason, incapable of making law enforcement more effective and pushing things towards the above described equilibrium, and instead responds by throwing more resources into the existing ineffective system.)

Are you aware of any research done on this question? Granted, Russia and Mexico have cops everywhere, but so does Singapore and Monaco.