The allure is that it's (initially) a simpler game, and thus easier to learn and play. It's faster than 1-h. Easier than snooker. Less strategy than 8-ball. Less complicated than straight. It's perfect for a a tournament format. You can luck 9 balls in and win.
That being said, you still have to be a great player to be a champion in 9-ball, as there are certain skills the other games don't necessarily require. Such as, many long distance position routes, loads of specialty shots, monster breaking under control, kicking to win, and superior shot making.
Other games are challenging on different levels, but 9-ball does have its redeming qualities.
-td