Is it possible the organization isn't reaching out to them? When I think of large companies in this area, I think of government contracts, etc. Maybe I'm a different fan demographic but they could give away Miller Lite steins every night and I wouldn't drink Miller Lite. 
I agree with you though .... the kids (mine did anyway) love bobble heads, towels, hats, etc.
As a government contractor, these corporations don't advertise much. The business model is to respond to a gov't RFP and win the contract. Advertising and corporate sponsorships won't help win an RFP. Also, on a federal contract, the profit amount is limited and there isn't the millions lying around to sponsor a stadium.
Agree with you on Miller Lite. Blecchhh. But the masses lap it up; it's truly a horrible product.
