> Complex societies exist and work.

They certainly exist. Whether they work is rather the question.

> Everyone who has a choice makes the choice, dominantly, to stay in them.

Which people actually have the choice? If a group of people want to stake out a piece of land somewhere -- even if they pay for it -- and then try to operate some kind of self-contained society there without being subject to an existing government's laws or taxes, what happens to them?

There isn't a lot of land on earth which no existing government claims is its jurisdiction.

> Imagine a system with competition but no taxation. You lose public services.

You lose tax revenue. That isn't the same thing.

Suppose nobody is maintaining the road in front of your house and there is a huge pothole, or the road isn't paved to begin with. You and a few of your neighbors, with nobody forcing you to, agree to split the cost of paying to fix it so that people can get to your house. Maybe you even just pay for it yourself because the thing is right in front of your driveway. Attempting to charge a toll or something is pointless because there isn't enough traffic to justify the administrative costs and you just want the pothole gone. Does this have a different set of benefits and trade offs? Sure. Are there still various roads that are open to the public? Yes.

And then you have to ask whether having a third of your neighbors not chip in to hire the paving company costs you more than having the government pay 600% more to have it done as a result of various corruption and administrative overhead.

> Same for competition without private employment–you're in a totalitarian state with a monopsony on labour.

A canonical example of the absence of competition.