You can’t use conference championships until all of the conferences use the same method of determining their champion, and have equal number of teams in each conference. Big XII, SEC, ACC, etc. have a one game playoff to win the conference (East -vs- West, North -vs- South, or Atlantic -vs- Coastal). Other conferences do not have that (Big East, Big 10, etc.).
That’s an extra week of rest for those teams, and one less chance to screw up a good season by possibly playing the 2nd best team in your conference.
To have playoffs, I think you’d have to start by evening out the number of teams in the conferences. Then the conferences could be almost like divisions in pro football.
It’s a good thing you used pro football as your example, instead of, oh, baseball. Major league baseball uses division champions, and doesn’t have balanced divisions.