The math doesn’t work with 12 teams.... you end up with 3 teams left standing after the first two rounds are played. If you want more than 8 teams in, you gotta jump to 16 to make the math work.
I drew up the "Solution" on paper many years ago. Take the top 16. Play them at bowl games each week. (So the big bowls would rotate semi finals as they do now) and the other 11 games would go to the oldest standing bowl games. Played from seasons end through december. On New Years Day you could have all the crap bowls during the day while people recover from hangovers, and play your title game at night.
Fans will still argue about #16/17/18 but its a better argument the number #4/5/6
Fans would be thrilled
Bowls would be happy
Networks would be estacic
