I've never been to a festival where the policy was as strict as Peter mentions above, with bags searched, etc., but many US festivals are held on park land or at venues where the administration/owners have a no-alcohol policy, so the festival producers have no choice but to comply.
The Washington Folk Festival is held at a National Park site which bans alcohol. One year the suggestion was made (by me) that we should see if we could get a nearby tavern to be a site for pub sings and the like, as many festivals in the UK do. This was squelched immediately by those who said they didn't want people going "off site" (even by the 20 feet or so this would have involved), and they feared the Park Service wouldn't like it (not that they were even asked). So that was that. It's still a good festival, though!