Yes, police have the authority to use violence; that doesn't necessarily mean they have to have some sort of essence of violence that drives them to be violent all the time. Indeed, police in many situations do successfully negotiate situations without employing violence. So, clearly resolving situations peacefully is possible even while maintaining the capability of violence; just, often the police have no particular incentive to do so.
Indeed, you can look at the military; soldiers are also violence workers, and yet they seem to be much better at not being violent than the police are, staying disciplined and not firing until the rules of engagement allow them to, where the police seem to often start shooting as soon as they get a bit scared.
The problem is there's hardly any accountability; the feedback loop is horribly broken. A police offer's incentive ought be to employ violence precisely and only when it is called for. To, y'know, correctly use their judgment to discern in the moment what action is most appropriate. It is far from impossible! But since there's minimal accountability for police, well, that's not what happens.
Yes, they are pretty good at RoE, and when it's time to shoot, they shoot the hell out of their target. But their job is distinctly not to spend all day in pursuit of individual criminals and apprehending them.
Military tries to avoid contact with criminals until it's fireball time.
[0] https://theintercept.com/2020/06/03/the-rebellion-in-defense...