Is there somewhere where ideas like this are discussed intelligently?
I'm not aware of a single central hub for such discussion I'm afraid. There's academic work in the area of development economics which looks at countries around the world and tries to identify what traits of governmental institutions seem to correspond with economic growth and prosperity. This is where Paul Romer and his charter cities idea is coming from.
If you want some really out there but intelligent discussion of related ideas you might want to check out Unqualified Reservations. Maybe start with the gentle introduction series. Mencius Moldbug could be described as many things but concise is not one of them so you're looking at a fair bit of reading there.
Arnold Kling blogs on this topic a bit as well, he has a particular interest in the idea of 'unbundling' government services.
If the experiments in governance are atheoretical, then I'd expect most of them to be worse. Just as most random mutations in a complex organism are likely to be worse.
Think of competitive government as a meta-theory of political mechanisms in the same way a well functioning market economy represents a meta-theory of producing efficient organizations rather than a theory of how to run an efficient organization. The question is how to structure things in a way that there is an incentive for good governance. If you get the incentive structure right then good governance will tend to outcompete bad governance. The individual experiments would not be atheoretical but the structure under which they operate is intended to be agnostic about what the best approach will prove to be.
Many of the people you'll see talking about competitive government are libertarian leaning and so would have their own personal ideas about how to run a government but rather than privileging their own pet theories they want to put them to the test against other ideas about how to run things. A Thousand Nations emphasizes that traditional ideological opponents could in theory both get behind the idea of competitive government as it would give them the opportunity to go and test out their own utopian ideals without having to convince anyone else.
Experimentation has a cost, what is the expected benefit from experimenting with different forms of government. How is that expected benefit justified?
I don't see how this is any different in principle from the question of the value of experimentation and innovation in general. Many technologies ultimately prove to be market failures but I think the evidence is pretty compelling that economies that follow a free market model and 'waste' resources on ideas that don't pan out have a better track record of producing net benefits through innovation than economies that attempt to centrally plan innovation.
I just find it disheartening when people don't want to try applying their brains to the problem of at least narrowing down the space of how governments should be designed.
I don't believe advocates of competitive government are generally doing this. They just don't believe that their own ideas should be given special privileges over everyone else's.
Patrissimo argue that we should try to design good mechanisms for governance rather than try and use the current broken mechanisms.
I agree, however we don't have a theoretical framework that we can use to evaluate different systems that are proposed. Ideally we would be able to crunch some numbers and show that a Futarchy responds to the desires/needs of the populace better than "voting for politicians who then make decisions" or anything else we come up with.
So we need to be able to do things like quantifying how well the system responds to the people. Pretending that humans are agents which have a utility function would seem like an obvious simplification to make in the model. We also need to formalise "being in charge".
I tend to formalise who has authority in a system as a number of pairings of people and posts. Posts might be the seat in the senate or the presidency, although we will want to expand this notion of post to look at all bureacracy and how they are filled.
One way a proposed mechanism would work would be through controlling the pairings. Futarchy suggests that we might look at other ways to make the mechanism work. This would be quite hard to model, we would have to model the incentives of the people making the prosperity indexes and the incentives of the market participants.
So we want a system that selects the people/post pairing that maximises the groups utility function, while assuming that the people in control of the post will maximise their utility and everyone else will try to (ab)use the mechanism to maximise their own utility.
Does this seem like the right track?