To start with, standard chess in its current form has been the standard for a well over a century. It is well known and well established. It also enjoys a fair amount of popularity. It is widely seen as a test of intellectual prowess (even if that prowess often fails to transfer to other fields) in which luck has no effect in the game (even if that's not 100% accurate).
Assuming the Wikipedia article about Chess 960 is accurate, Fischer announced his variant to the world in 1996. Thus 960 is still relatively new and unknown. While I've been playing chess off and on for 45 years, I've still never played Chess 960, nor even watched one game. I suspect that if you asked the average person on the street what Chess 960 is, they wouldn't be able to provide an accurate answer. I also believe that a lot of people wouldn't like a game in which the pieces start in different positions every time; especially one they've already known which always starts with the pieces in the same positions. Additionally, luck can play a part in the game, which takes away from the purity of intellectual prowess that attracts some to chess.
Overall, this is my way of saying that standard chess remains popular; I'm certain it has more broad popularity than Chess 960. Also, it is a more established history than 960. Time will tell whether 960 increases in popularity, stays an interesting variant of the standard game, or turns out to be a fad. However, given standard chess' head start, I believe it will continue to remain the standard for the foreseeable future.
Also, as noted by lenik's answer, chess is enough of a challenge for most of us who play it.