The problem with this is that like
@fez says above. That doesn't benefit the people at ground level who have no-where to live and can't afford the food. It's more difficult on an Island because in places like NY or London, the locals at least have the opportunity to move further out and maintain ties with their families etc and commute in for their jobs from more affordable areas. It's still not ideal and it's a shame anywhere nice ends up only being a habitat of the rich.
Without some kind of action it doesn't matter how many tourists go to the island because there'll be no locals there to work in shops/bars to serve them. You then end up with 2 outcomes
1 - The tourism industry dies. Then the government do what they can to attract people back again when it's too late
2 - You stop things like Air bnb's etc, limit holiday rentals to hotels/apartments and make normal residences available for residents only.