Their premiums would go up sure but that would be offset by the additional income received via beer sales. There is a reason why every other major sport serves beer...it's profitable. As far as drunk people in the stadium, I think it would actually lead to less really drunk people because it would cut down on all of the people sneaking in hard liquor. Most people that want to drink at games find a way to do it. Allowing beer sales would just make it move convent for your average fan to have a couple beers and allow LSU make some some money off of it.
Hopefully they wouldn't gouge like Jerry Jones does. We went to the OU game at the new cowboys stadium a couple weeks ago. 8 bucks for a 16 oz Miller Lite. Your only other choice? a $14 wine based margarita. popcorn? 10 bucks!