What's a " true" system ? If humans are part of the selection process it's still subjective. Changing the number of teams doesn't t change it. The conference championship games are pretty much quarterfinal games anyway. At least those are merit based and not picked by a committee.
Then build on that.
The P5 now all have conference championships. Expand the playoffs to 8 teams. The 5 conference champions get in automatically. The next three teams are picked based on overall record. If there’s a tie in record, go to head to head matchup if that happens, or if it didn’t, subtract the average points against from the average points for. Rank in order of highest numbers.
Everything is in the hands of the teams, and everything is skewered towards good teams.