Tempering and refining intonation are the main reasons given for them. (Look at the saddle on any guitar and you see the principle in action, less pronounced.)

My reason for liking them (Avian to be precise) also include why (using the two American big name guitars) Martin are seen as having a richer bass whilst Gibson can be sweeter at the treble end. As fan frets have a longer bass length (Martin) and shorter treble end (Gibson) you can get the best of both worlds.

Obviously, far more variables involved but for modal tunings with a low bass (down to C on the Avian with no wobble) they are stunning.

Try not to look at the guitar first time you try one though.. You make no finger adjustment but it can look weird at first.