Good post. I think the biggest problem with a playoff would be establishing the teams that make the cut. Unless the procedure for establishing the teams was an objective freely examined algorithim the same problems would arise.
In basketball the committee picks 65 teams to make the field and there is still controversy every year when some bubble teams are left out. Imagine the uproar when only 8 or 16 teams make the college football playoff and 2 loss OSU or ND team makes the cut over a one loss SEC or Big-12 team.
The main problem now is that there is no clear definition of what being ranked #1 means. Is it the team that is playing the best right now, the team with the best record or the team with the best winning percentage * strength of schedule?
The system I envision would eliminate that, as the schedules would do it. Specifically:
Align the country into 16 conferences of either 12 teams (lowest impact on existing conferences) or of 16 teams each (largest number of eligible teams).
Each conference is then aligned into two divisions. Each conference has a one game playoff to determine their conference champion. Only conference champions would be eligible to move on into the play offs.
Conference schedule would be eight games plus one for the championship. Thus 9 games played and 16 teams going on in the playoffs.
The devil is in the details though.