Bowl access is the tip of the iceberg. The Big EAst champion, in the entire history of the conference, has never had a contract bowl home. It still doesn't. What This is a problem that the conference needs to address.
The access - is to the revenue sharing system, not to any particular game. It's about money, and always has been. This is the cartel of the current decade. The college football POST season revenue sharing around scheduling of games.
The cartel in the 80's-early 90s was built around the television broadcasting revenue sharing of the regular season scheduling of games. The bowl system took over, with the evolution of the Bowl Alliance system, which involved the creation of the Big EAst football conference, evolving into the BCS, which is now evolving into a pseudo-playoff.
What the current system of quote/unquote "access" to the bowl system entails - with a group of conferences all having automatic appearances, adn another group of conferences all vying for a limited access - is an accurate reflection of the revenue sharing plan for the college football post-season. the cartel is no longer the CFA, it's the loose group of conferences, that are bound together by post season contracts for game.
THat cartel has price fixed what their games are worth, and what the other games are worth, based on the total of what they are taking in from ESPN for the post season.