The state monopoly on violence (+ a judicial system) tends to result in a low amount of violence... at least intra-state. Wars are another matter. Notably, there is no monopoly on violence between states. States are allowed and somewhat expected to be violent psychopaths externally.
Internally as well, given what happens to any push back against law enforcement where I live- in the US, at least, if you try to defend yourself against state violence you'll be summarily executed in the street.