Anarchism

Yes it is what you said.

The police in all countries exist specifically to do violence against citizens of that country. That is literally their reason for existing.

You said they're there to carry out violence on citizens. That's not what the police are or should be for.

If you have services available other than the police, it is in your interest to prefer those.

No. You're again thinking police are violent thugs everywhere.

it is in our interest to offload non-violent services from the police onto social workers and other non-violent labour.

That doesn't make much sense to me.

My wife gets sexually harassed at work... is she just not supposed to call the police? My car gets stolen... am I not supposed to call the police? I see a policeman in the street and I am lost, is it wrong to ask for directions?

I appreciate that the police may be far more militaristic where you live, I acknowledge that I'm lucky in that regard, but you should at least acknowledge that that stuff varies place to place. I don't think the belief that police should be/are only "violent labour" is a correct one.