"Who is truly the best" is settled in the playoffs/championship in every league--not by who beat whom in the regular season. That's, per game, meaningless.
Relegation is something else entirely---relegated teams play in a lesser league, not in the 'other conference" in the same league. It's quite the opposite of what you are imagining...
MAybe the NFL should make all teams share their draft boards? Like, you know, so they don't draft Mitch Trubisky over Mahomes, for instance?