Why might an Island be a good setting for a play?

Because an island is a "closed" limited space, with limited opportunities for contact with the outside world, the playwright might feel freer to imagine a society quite different from any that already exists. Think about the novel Lord of the Flies where a group of schoolboys are stranded on a desert island and begin to revert to a much more brutal way of life where the unpopular child, can be killed, not just bullied. The same would apply to a play. The smaller and more isolated the island, the greater the chance of the society "going its own way"!