Doublem23 made an additional point that I thought was interesting when he referenced the "85-win purgatory" that the White Sox seem locked into. He talked about how young teams opting to rebuild often feature a group of young players who, in spite of their struggles upon reaching the Major League level, are given ample time to mature as a group, eventually forming a core of solid veteran players that remain competitive for the balance of their careers. I mentioned the example of the Braves in another post. I'd also submit that the New York Yankees' early teams under Joe Torre featured a similar group.
(Their spending didn't increase until the bidding war for Jason Giambi prior to the 2002 season. For anyone who hasn't done so, I would encourage you to read Joe Torre's book The Yankee Years. It's an outstanding read, and it discusses the shift in the philosophy of the Yankees organization following the loss to the Diamondbacks in the 2001 World Series. Torre believes that that loss was what spurred Steinbrenner to spend such large amounts of money, as he couldn't accept being second best.)
The White Sox haven't had a "young core" for more than twenty years. Their most successful youth movement occurred during the early 1990s, when Frank Thomas, Robin Ventura, Jack McDowell, Wilson Alvarez, and Alex Fernandez were around. I would actually be interested to hear Robin's thoughts on that group, and if he believes that the Sox have a chance to assemble such a group in the near future. They have talent at the lowest levels of their farm system, but the upper levels are largely a barren wasteland. It will be some time before said talent comes to fruition, which is by no means guaranteed. And, as Lip pointed out, Sox fans aren't exactly the most patient group when it comes to allowing ownership dismantle this team. If the Sox decide to scrap the current roster and start over, how many fans will be left by the time the refit is complete?