I think you overestimate how rampant murder is in the populace. Police do not deter murder... consequences deter crime - to the extent that they can deter fundamentally irrational actions. Police are also genuinely bad at *solving* crimes (check homicide case closure rates).

It'd be a bit of an exaggeration to say that the only days police don't deter me from murder are when I have zero in-person interaction with the public. But only a bit. The consequence deterring me is organized and armed response. Anything less and I'd take my chances.