I could definitely think of *worse* ways to spend $10 million (if I had the money).
I think I would enjoy a private island, but not as my ONLY residence. I think I could enjoy spending summers there, and could imagine only venturing off-island once a week or so for supplies, etc. However, most of the islands I've seen on those shows are small and pretty flat. I would not want to be on one during a bad storm. And it would also depend on the "amenities" of the island. My sister owns a lake house (not on an island). There are a couple of privately-owned islands on the lake, but the houses on them aren't hooked up to electricity, plumbing, water, etc. I'd much rather have a non-island house with all the comforts of home, rather than a primitive cabin on an island.