What is the appeal of the fixed lens cameras?

Clearly the X100 series are a phenomenal success.

I'm just wondering if you guys can distill down for me the chief appeals of buying a fixed lens camera over a mirrorless with interchangeable lenses which is arguably far more versatile?

Is it a question of compactness? Portability? A stylistic choice? Does having a single lens to work with stimulate creativity by making you work with what you have, rather than constantly wishing for different lenses?

Discussion only, I'm absolutely not trying to start a war! I'm just probably out of date having only recently moved from DSLR to MILC, and been surprised at the popularity of these fixed lens offerings!

Go!!!