You're being pretty hyperbolic. Private security is already used in many places around the world, including America. No matter how strict of a police state you live in, safety is always going to be your own responsibility, and police are always going to be a tertiary preventative measure against violent crime.
The irony is that in some places in America people ARE armed to the teeth with kevlar and shotguns because their local "highly trained scrutinized government team" takes hours to respond to active home invasions. The argument for private security doesn't solely come from a place of mistrust in police, it has it's own benefits not limited to much faster response times.
The police can remain as a government organization, as we're not advocating for anarchy. They can be an interface for the judicial system and will have the power to oversee private institutions to make sure they're not acting out of bounds of the law or constitution, but the police street enforcer is an obsolete/outdated concept that
clearly needs to be improved on.