Since every country claims a 200 nautical mile exclusive economic zone already, it's pretty unlikely that a new island will form that far from existing land.
Indeed, but most of it is very deep and won't be seeing any new islands soon.
Also see wikipedia "principality of sealand". Some british nut tested a lot of the legal precedents. Short version, it totally works, although there was that one time his nation was conquered by mercenaries hired by a german lawyer, and his son was taken hostage. So, self defense is a very real concern.
Given that, there is no benefit to leaving exclusion zone. You can just set up in international waters much closer to shore.