Sneaking in booze is unbelievably easy, done it many times and never was worried about getting caught. Grab a couple of 1 dollar whiskey shooters, buy a pepsi from the concession stand and your money.
As others have described before about having to be there so early and still get a bad seat sometimes is the reason why I didn't get tickets this year. For people like me who are actually of legal drinking age, it's fun to go downtown and mingle with other people before heading to the stadium. What it really boils down too is it's actually pretty annoying, more than half the people around you could care less about the game, and are just there because it gives them a reason to drink.
Especially for those who like to tail gate before every game, we had to get up around 7:30 just to be able to get 3 beers in before we had to leave for the stadium. After two years of doing this, it just got old. I love being at the games and I love the game day atmosphere but the extra hassel that general admission seating brings to the table makes it horrible IMO.