Great responses to this thread, and many were very enlightening to me!
A parallel to pool's popularity with children who grow up in Asian or Pacific Islander countries would be baseball in the States. Children in America are turned on to baseball and/or softball at a very young age.
As such, Americans dominate, in most instances, the sport of baseball, most likely because of the American TV exposure. Many young'ns grow up watching baseball greats like Cal Ripken, Jr., as an example. They want to play baseball because of it.
Ice skating elevated to new high after the Kerrigan-Harding scandal. People were hungry to learn more about the players, and in the process, ice skating enjoyed new heights in popularity nationally and internationally.
Pool as a "sport" in the United States may grow if given the right platform. To date, though, NFL, NBA, MLB, PGA, and tennis seem to dominate ESPN and other sports channels on American TV, and as such, pool has had one tire in the sand.
There is a new era up ahead with the trend of higher payouts. Hopefully, it will provide players of all nationalities the drive to push forward, and in the process, the popularity of pool, at least in American culture, may grow because of it.
JAM