For example, if a town's police system disbanded, but the state police still enforced laws against members of the town preventing them from engaging in their own policing, that creates a different scenario than if the state police didn't enforce any laws against the members of the town acting like the previous police force did. If even the military refuses to touch the area, given a threat that would normally allow the military to act like a foreign invasion, then it is a different situation compared to when you have a lawless area that's still protected from external threats.
And then you have lynchings like with Ahmaud Arbery. Not a thief, still shot and killed. Vigilante "justice" is often not just.
Though you may be right, an increase in lynchings may overall reduce crime (as presently defined, and excepting lynchings). It will also probably have a lot more false positives than the existing system, increasing paranoia with respect to outsiders and "others". So crime in a community may go down, safety for outsiders will likely go down, and for insiders may go up.
Suppose whichever police force(s) you're talking about shall be disbanded. In this experiment, you can choose some amount of delay between that announcement and the actual disbanding; whatever seems most reasonable to you.
How would that play out in the following days / weeks / years?
How do you think individuals, companies, insurers, etc. would adapt? What aspects of life would be better, or worse?
(Personally, I think society would be for worse off. But of course I'm only guessing, and could be wrong.)