What do people need to carry into the stadium in bags/backpacks/purses? Unless medical in nature, if you can't get by with just having money/keys/phone in your pockets for 4 hours then what the hell are you doing there?
Anytime I go to a game with my wife (any sport), she normally just brings some cash and her phone (and driver's license if we are going to somewhere that servers booze).
If you have to bring a diaper bag or a bag full of "stuff" to entertain your kid, then your kid probably isn't at the right age to go to a game (saying this as a dad).