We tried private ambulances and that is an ongoing disaster, what you are describing is a personal army or guard, look at history to see the plethora of problems with those...

Not that Police are perfect, far from it, but I'd rather a force I can sue in court and protects me from my enemies even if I'm broke than a private militia.

You could have Police-As-Contractors I guess but unless that comes with some legal innovations that just adds another layer of bureacracy.

Objectively terrible idea.