1> Patrol public spaces to deter illegal behavior in those places, direct traffic, punish traffic offenders, offer directions to tourists, etc
2> Respond to calls from citizens, investigate the crimes that those calls are about, locate and apprehend the associated criminals.
I've only lived in places sparsely populated enough that <1> is mostly impractical except along highways and around major construction sites.
The VAST majority of the value provided to people by the police clearly comes from <2> - it's the reason that no sane person would mug me (or kill me) for $40 cash on an unpatrolled country road, or invade my home and take up residence there against my will. 99.9% of citizens benefit from <2>, as it's the main deterrent to any antisocial person coming and taking whatever they have of value.
It seems to me (though I don't have data) that most (nearly all?) the mistreatment of (maybe mainly black) citizens by police that has been garnering media attention over the past decade or so, happens during the course of <1>.
Plainly, I don't believe in deterrence as effective or a substantial reason why most people don't engage in bad behavior.