What if that meant that people could fire their police department and replace it with a different one if they didn't like the way it operated?
That would depend on exactly how things were set up, but we do it with politicians who have all the same bad incentives to keep power.
Do you prefer mandatory arbitration to being able to use the public court system? That's a privatized justice system.
If the monetary damage was high enough vis-a-vis the ability of the public system to deliver me restitution for my losses, I'd very quickly be hiring private detectives yes.
See for example, "The Problem of Sexual Harassment and Forced Arbitration": https://www.correiaputh.com/news/problem-sexual-harassment-f...
Even law making and law enforcing please.
Governments are incompetent by definition and hold too much power. I'd rather have a N local corporations competing against each other and not being able to extract money from everyone's profit - compared to a massive monopoly governing and profiting off millions of people.