I just learned something new today. In a way the San Diego Padres organization is responsible for "God Bless America" being played prior to "Take Me Out to the Ballgame" during the 7th inning stretch at select games throughout the baseball season.
John Dever (not Denver) worked in the Padres' Media Relations department at the time of the September 11, 2001 attacks. Before games were cancelled he was called into a meeting to discuss how the attacks would be acknowledged that night.
Military tributes at baseball games: True honors or hollow gestures? - The Washington Post
At the meeting, Dever spoke up with an idea. The traditional "Take Me Out To The Ballgame" would sound out of place during the seventh-inning stretch. He suggested the Padres should instead play, "God Bless America." The idea reached the Padres’ Larry Lucchino, who had flown into Milwaukee for an owners meeting. He relayed the idea directly to Commissioner Bud Selig. A tradition was born.
That's about where the Padres portion of the article ends but the rest is a pretty good balanced debate as to whether honoring the military at ballgames has become a stale, hollow gesture. I, for one, like the displays of patriotism in general but think that the league gets carried away in just about everything it promotes so I definitely see the other side's argument.