We're talking about the super rich who won't, generally, be using public services, and will usually be making their own private arrangements, especially for the likes of healthcare where they'll travel to the "best" healthcare providers rather than rely on the local hospital on whatever Island they officially "live" on.
My point was that unless there is standardised tax agreements across ALL countries, the mega rich will always choose to base themselves in a tax haven where they pay less tax, maybe not the lowest tax, if say, it was a war zone or suffered earthquakes or hurricanes regularly, but certainly, if they could find a nice Island with good weather, flexible/convenient for travel (air or yacht) to more developed countries, relatively safe, etc., that's where they'd go.
Look at Tyson Fury moving to Isle of Man - couldn't get more convenient for getting back to the UK mainline, so also good for onward travel to USA, Europe, Carribean or wherever else he'd like to holiday etc. He's only gone to "live" there because it's a tax haven, not because he likes steam trains and trams!