The legitimacy of a playoff lies in the transitive law of equality or inequality (A > B, B > C, then A > C). Granted, this argument is tenuous because its about the best team that shows up that day, unlike a 7 game series like in MLB, NHL, or NBA. But if there was a playoff, theoretically the winner would be greater than all the teams in all the divisions that provide their champions to that playoff. This may not be completely accurate because the champions of their respective divisions will have losses to teams within their division, but the theory is that the best team in the division is the team that has the best record in that division. From that point, we begin the transitive law.
Take March Madness for example. Northern Iowa beats Kansas, MSU beats Northern Iowa, Butler beats MSU, Duke beats Butler. The transitive law says that Duke is better than Kansas. Without that tournament, and if Duke never played Kansas and they never played any common opponents, there would not be any on the court results to see who is better. As sports fans, we do not like reliance on statistics or computers to tell us who is better, we want to see it on the field, court, ice, etc.
Given logistical constraints of not being able to literally play every team, this appears to be the best way of doing it. Of course there will be arguments that injuries change the make up of a team (i.e. Kalen Lucas for MSU), but those things are part of the game. Additionally a long chain of who is better based on common opponents is tenuous, but there doesn't seem to be a better way of doing it and if you keep the time interval between each match as short as possible, it gives it more legitimacy. Without a playoff, we will have another USC or LSU national champion situation in the future.
