Actually, I'd give automatic bids to all conference champs. Just like hoops. That would be 11 automatic bids/ 5 at large bids.
I don't think it's feasible to have 3 rounds of football playoffs at neutral sites. The travel cost alone would be almost prohibitive. Each school's allotment for the Sugar Bowl is 17,500. Even the cheapest tickets go for a few hundred dollars, I believe. Not many schools could have that many fans who could/would travel 3 weeks in a row to neutral sites.
The NCAA tourney early rounds do not always sell out. I've bought walk up tickets on game day on a couple of occasions ... for $35, IIRC, for 2 games.