The majority of the tournaments are held on public parks fields. Most municipalities have strict rules when it comes to alcohol being served at their facilities. I doubt any Tournament Director would want to jump thru all the hoops needed only to have inebriated parents running around the fields.

The Lockport Canal Days festival comes to mind. They have a cordoned off beer garden with controlled access. No unopened cans are allowed outside of the garden. There's a heavy police presence there.