Buying an island doesn't mean you can start your own sovereign country.
A lot of islands in Greece or Canada have been sold to private owners but they are still part of their countries.

An island is no different from a simple plot of land, it just gives you a fake feeling of independence with no real borders or fences in sight. But in reality there is no difference.

It's like we start discussing if we should plant either strawberries or corn on Neptune before we even get there.