Paul at Nice Guys Finish third says he's tired of "God Bless America" in the 7th innning, pleading "Please stop policitizing my baseball!" I suppose that means we should do away with the National Anthem at the beginning, too?
No, the reason to stop singing "God Bless America" during the middle of the 7th inning is that continuing to do so trivializes the sentiment that started us singing it in the first place. It has stopped being an expression of our solidarity in crisis. It seems like it's just another opportunity for celebrity showcasing. To continue singing it dillutes, I think, the poignancy of the song, and the solemnity with which we remember September 11th.
In addition, the 7th inning stretch has traditionally avoided a serious tone--we stand up, stretch, belt out a low-brow bar tune, which is more fitting for some fans depending on how many beers they've consumed.