I take it by government you mean the state (two different things).
That said the state didn't create property, scareness and humans did. As long a person worked or got lucky and found a scarce resource and said this is mine, that is private property. That is its origin, the thought and the community/society's recognition of the concept that ______ belongs to _______, that is all private property is. So to claim it only came from the state shows to me, you have no realistic base to what you are trying to discuss.
Yes I've heard of Pinkertons, also heard of sheriffs in the wild west who were largely private employees of the populace in unincorporated territory.
We don't need government police to defend us, well that isn't their job, but I agree we don't need them and I am sure I could show you historically that government police have always had the primary job of generating income for the state more than protecting anyone.
You asked me how I would solve security, I told you private security, you've yet to explain how this is not feasible.
I would say the state police is the haven of psychpaths and sociopaths that you are afraid of, and the current state of the US police force, across the nation, affirms that sad state of affair. If you would have me believe that having a private security service that is beholden to the law they are paid to enforce, that doesn't control the system so that they alone are responsible for investigating themselves, prosecuted by DAs who they work with, and their proceedings administered by judges who are usually former DAs, is worse than the state system implemented in western society today you are going to have to actually present a solid argument.