So what are the functions which are unique to a police force, which wouldn't be better served by some other type of professional? I recognize the following.
Literally nothing, ask a cop who got out of the bastardry:
https://medium.com/@OfcrACab/confessions-of-a-former-bastard-cop-bb14d17bc7591. Arresting suspects following a report of a crime, which should only be necessary in a minority of cases in our modern age of surveillance. Can be revisited if we dismantle the surveillance state.
Why commit crimes after the massive police budgets are pumped into projects which educate, feed, house, and heal communities?
2. Responding to reports of violence in progress, with the intent to minimize harm to everyone as much as possible, including suspects
Cops don't do this except so rarely it might as well be accidental.
3. Partial involvement in investigation
Cops aren't trained for this, it presumes the presence of crimes that wouldn't exist without motivation, desperation, frustration, and lack of medication, security in food, security in residence.
As I understand, this is a minority of what police actually do, and it seems to me like restricting them to specifically these duties with appropriate cuts to size/funding would be incredibly dramatic. Not abolition, no. But it would be a dramatic departure from police in their current form.
A pseudo-military branch which was empowered and trained to identify, locate, and prevent outside actors from harming their communities when possible, or if necessary intervene to neutralize threats to their communities already in progress would be the closest remnant to our current police forces... and that should be fucking alarming as shit when you realize what we actually have are not tasked with preventing harm to the communities they work in, are not tasked or trained to prevent shit before it happens, but are definitely equipped like a pseudo-military force.