Tell that to the 17th team.
The opposite: the larger the field, the more teams that almost make it, as the expanded NCAA tournament field has demonstrated over the years with more "bubble teams" and more disputes.
And the major conferences would never agree to conference champs only because the disparity of competition in different conferences is so great.
Do you remember when the NCAA tournament field was only 12 or 16 teams, mostly conference champions? Far fewer disputes then than now with 64+. There were years and years where the only SEC team to make the tournament was Kentucky, but no disputes since only one could go, and the basketball talent was more evenly spread than football talent.
No system will end disputes, they just need to decide how much to expand the NCAA football championship field beyond two teams.