Did you mean a tropical island? Or an island in less tropical climes?
Iceland is an island. Likewise the Hebrides (both Inner and Outer) and the Orkneys, none of which are tropical.
(And I know you mean your own private island)
HAve you ever lived in the tropics for an extended period of time?
I lived on Oahu for almost 3 years.
If I ever had a hankering (which I never did) to live in the tropics, even on an island, that cured me of it forever.
High humidity (which you are probably used to)... I always felt like a soft green mold was growing on me.
Giant insects INSIDE your home...huge gross centipedes right out of B horror flick...cockroaches that could carry you off. Yikes!
And living on an island? ... I got "'Rock fever" about the second year. But that could happen on an island in any clime.
It was especially bad on Oahu because unlike those islands right off the coast of Scotland, Hawaii is a couple of thousand miles from any sizeable chunk of land.
So: No, thank you! We don't want any tropical living with or without slushy drinks or toes in pools!