1. As far as I can tell, police forces are a quite recent innovation in the Anglosphere. 1900-ish.
2. When seconds matter, the police are only minutes away.
3. Power corrupts, rather automatically. Police, video-cameras, etc.
4. Top-down law is, to a 99% accuracy, simply a method for government to screw people.
Solution: Deputize EVERYONE. Abolish the formal police force.
FWIW, I think that the Concealed Carry movement is motion in this direction. If you carry, you're self-deputized. I consider this a much safer world than if the police are the only folks with guns.