There're a lot of reasons why SFIII is unpopular, but the main reason is arcades and 2D fighting games in general "dying". For istance, I could never get to play SFIII until some years ago, when I emulated it.
That said, I think there's a lot of underdog fanatism around the title. I honestly don't think the cast is that good and, in my opinion, the game has aged badly. There's a lot of nostalgia when people talk about SFIII. Not saying the game is bad or anything like that, but it's not the second coming of Jesus and the cast is not plain better than that of SFII (In fact, I think it is vastly inferior, both from a gameplay point of view and from their design).
I still would like to see some SFIII chars in SFV sooner than latter.