Going somewhere doesn't mean it adds culture. Is anything new or interesting happening at the eagles games? Anyone gaining new incite or having revelations over the human condition? Seems more like people are just eating the same-old food and yelling at one another.
They literally are part of the culture. "The same-old food" is also culture. You are describing culture, and then saying "that's not culture". I think you're just using the wrong word for what you're trying to communicate.
The stadiums aren't contributing to that culture. They serve mass produced commodity food that's ubiquitous. I concede that hot dogs and the history behind them is culture, as are interesting new variations or applications. Though, continued sales at stadiums isn't adding to the culture.
Culture isn't history. We are constantly creating new culture. You don't have to like it. There's lots of new culture I don't like. But you can't redefine culture to mean "historic stuff, or stuff I appreciate".