Interesting discussion and the points are valid in my opinion especially the part about the Sox not consistently winning but I also think part of the issue is that the franchise has refused to take on the Cubs directly.
Chicago is the White Sox home too but they don't seem to act like it. When they've had chances to make serious in-roads (because the Cubs were floundering) they have refused to do it. I can't recall anything along the lines from a marketing or advertsing standpoint since the "us vs. them" campaign.
As far as the neighborhood perception, that's not a new issue. The race riots of the mid 1960's coupled with the location of the ballpark fueled that notion and it's been with the Sox ever since. In that case it's not the franchise's fault, they certainly had no control of the social issues of the day.