I think the difference being a team in a Conference chanpionship game could lose their 13th game and they still have a chance for a championship, and in some instances winning that 13th game could be what even gets them into the playoff and gives them a chance for a championship. Both are distinct advantages for their 13th game versus NDs 13th game being win or go home.
Conferences existed long before they started playing conference championship games, and some teams in the lesser conferences go a whole season without playing a legit top 25 team, but yet can be rewarded for winning that 13th game. I understand both sides of the argument, my point is the 13th game being a playoff win or go home versus the 13th being a conference championship for some school that played two directional schools that season are not apples to apples.