Many variations on this have been tried. It's doomed. Look at
existing national governments in, say, South America, vis-a-vis the US government. The US government is,
de facto, an imperial hegemony. It's not (quite) fully global but it can be fairly described as hemispherical.
Related:
Sealand
Kailaasa
[video]https://www.bbc.com/news/entertainment-arts-55092341[/video]
List of micro-nations
How to claim your own island
There's a famous one whose name is completely escaping my mind... group of Americans purchased an uninhabited Pacific Island somewhere in the Asian side of the Pacific and tried to set up a colony there, including requesting formal recognition as a country. If I remember correctly, a national military (Chinese?) ended up just occupying the island after they had done some developments on it, and they were just forced off the island. There was no recourse. If anyone remembers the name of this island, please post it... I simply cannot remember and web search is useless for topics like this.
UPDATE: cjm pointed out this this was the Republic of Minerva, it was not in the Asia-Pacific, it was north of NZ...
The sad fact is that most of these projects are started by and initially attract people who are just interested in doing illegal things they can't get away with in their home country. "No laws!" immediately attracts the worst-of-the-worst. A prison is also a place with no rules (when you really think about it) and the people who rule the roost there will always seize the dominant place in any such project, even if it is well-intentioned.
A more realistic alternative is
seasteading. Because a seastead exists for some profitable purpose (it is a business, not a "government"), it's not just about "no rules, man!" or (what is the same) "our rules, man!" So the rule-sets that will tend to emerge will be like business policies in the important sense that business policies tend to converge on prevailing market practices. Most people expect to take a lunch break at work, and most employers provide this even if the government doesn't make them do it. So the concept behind seasteading is you have a market of competing seasteads and the policies that emerge will tend to converge on a rational set of rules/laws. In the terminology of economists, the current market in statutory laws is thin, meaning, "customers" (citizens) only have a tiny handful of choices to pick from. But if the market were
thick, then we expect the producers of statutory laws (or business by-laws, just depends on how you think about it) to converge on customer (citizen) demands -- thick markets produce what customers want because customers have a lot of choices of where to buy from, so they don't have to put up with BS...
