I’m not sure what you mean by booking the field, but if anyone is getting money out of the deal, it’s the association. Hosting the championship games is a statewide recruiting advantage and the colleges with the largest athletic budgets can afford to pay more for the privilege. Being public/private has no relevance. It’s who can scratch the largest check.
Due to some state rules there are reimbursement for employees that work the event but the school gets parking. Do not think it is really a school thing.
Duke and Wake have been the most supportive especially Wake when they first got the games.
NC State torn down the field house two weeks before the title games in 2005. Remember the teams dressing in tents on top of the hill where the Murphy Center is now. Had the big blower heaters. State would not put off the tear down for 12 days. Should have moved them that year.
Four title games you can get by with one venue playing a game on Friday night. That should be either the largest attendance expected game or the teams that are nearest the venue. More than four you need two and seven or more it makes sense to go to three but it can be done with two. Three games on Saturday requires a noon start at the latest. 3:45 should be the secon game and 7:30 the third but that is still tight and would be a logistical nightmare at Wake if they only allowed the field house to be used for dressing rooms.