I am arguing that the police investigations and the justice system must exist. If it can exist without taxation, great. Otherwise, localities should tax as necessary to provide for police protection to their localities.
Local taxes are not an unreasonable thing. Local government is much easier to control. Not only that, but it is relatively easy to move if your local government gets too bad.
If you think you can operate a state without police investigation and a justice system, then explain the method and I'll sign on. However that kind of decision should be up to the local governments.
I hope I haven't given the impression that I have it
all worked out.

Here is roughly what I'm thinking: (1) People pay for their own
defense, or provide for it themselves. This means that police don't roam the streets looking for people to bust. It's also not much different than now as far as you or I are concerned, since the police will never intervene and prevent you from getting murdered. (2) If you want to press charges for a crime, you go to a state court (private courts could be used if the parties agree, but the state court is the only one with the power of true enforcement). (3) if you don't know who committed the crime, you pay for your own investigation. (4) the party you are charging is invited to attend the trial, but is not forced to, since they have not yet been convicted of a crime. (5) If the person is found guilty, they will be forced to pay reparations plus any police and court costs. The state police will go "get" the person if they will not report voluntarily. (6) If a person is ever arrested prior to conviction by the police, or anyone else, this is treated as a criminal act if the person is found to be innocent.
A variation on this is one under which the police will investigate for anyone and their "overhead" for this service is paid for by convicted criminals. This is okay, but it means that people convicted of crimes are essentially overcharged to pay for this overhead. Still acceptable in my book.
Check out
this post for a description from another fellow. He has thought it through more than I have. His description is closer to the second variation above.
Charles