The issue I'm getting at is that when every individual has to act as their own(and their own kids) security force, that's more expensive than pooling your resources for some police!
If it is more efficient to pool resources (as I think it is too) then people in the market will pool resources (like most all companies that exists now).
I'm all about having local police only. A city can be a good little unit if the people care about the upkeep. If police are beyond 1 degree of separation you start getting problems.