One problem with open immigration is that it makes all these supposedly separate experiments actually interdependent, which tends to lead towards either: 1) them all converging; or 2) immigration restrictions.
For example, Social Democratia has a free-rider problem with respect to its neighboring Low-Tax Libertonia: healthy and prosperous people will go live next door so long as they're healthy and prosperous, but anyone who gets sick or ends up destitute will conveniently move across the border to Democratia for the social safety net. Social Democratia will have to either drop its social programs (converging with Low-Tax Libertonia) or institute some sort of immigration restriction.
Or, say Crime Preventistan sets up a really good set of programs, education, etc., such that there would be virtually no crime in their country, and they can have very minimal police and virtually no government surveillance of their citizens. But they live next door to the Wild West Republic, which spends money on neither prevention nor police, and its rampant criminal population enjoys carrying out cross-border burglaries, or maybe even moving next door to set up their outlaw shop in Preventistan. The Crime Preventistan experiment can't really happen unless they're able to close their border with the Wild West Republic and restrict who's allowed to immigrate.
In short, I think it'd be difficult to maintain any differences between countries in the face of complete lack of border controls (open immigration, free trade, etc.), because any differences between them would be arbitraged away as soon as someone found a way to exploit them.