I think even the Cubs have noticed this as well with the development of Clark the Cub. I also think the fact that Wrigley has become such a tourist destination has also helped the White Sox. Here's why...
Lets say past 20 years..
Cubs have averaged 35,000 a game of which 60% were tourists (20,000 Chicagoans per game)
Sox have averaged 25,000 a game of which only 5% were tourists (24,000 Chicagoans per game)
Of the 20,000 for the Cubs...10% under 20 (remember..Wrigley is known for Drinking)....2,000 under 20 per game
Of the 24,000 for the Sox...20% under 20 (More families at the Cell, kids days, etc).....5,000 under 20 per game.
I just feel that an increasingly high percentage of kids in the Chicago Metro area are growing up going to Sox games and not Cubs. This is why I'm noticing that out of towners who move to Chicago are generally Cubs fans..but those born and raised in Chicago are increasingly more likely to be Sox fans and not Cubs fans. I feel this phenomena is on the increase...
This may be a big boon to the Sox in the future and the reason why the Cubs are America's baseball team and not the Sox..but the Sox are becoming more Chicago's baseball team and not the Cubs.