There are not just a few 1st person games out there.
Look at this German blog: http://1stpersonblog.blogspot.de/
Even if you don't understand the language you can still see that there are quite some 1st person games available, new and old.
In my opinion not all settings or plots are suitable for a 1st person game. I'd have a hard time imagining The longest Journey without April and as a 1st person adventure instead. Or I can't imagine "me" (female, 28) wanting to become a pirate, lusting after several women or saving the world from Baphomet. Having other characters doing these things is a whole different story.
But Horror games for example can be far more shocking if the player is directly involved. Some mysteries (like Sherlock Holmes) work well as 1st and 3rd person adventures.
My personal choice are 3rd person games. I can't really explain it, maybe it's because a lot of 1st person adventures I played have been rather sterile.