It has nothing to do with power or the perception of power. It's simply about money.
Outside of Pitt and WVU, the Big East teams stadiums aren't big enough to exchange a home date with a major BCS program. Rutgers and Syracuse can trade home-and-homes with Michigan State and Illinois every year, but if they want to add Ohio State or Michigan, they need to add seats and field better teams.
FWIW, Ohio State was going to play Syracuse, until the Cuse went into the toilet and Ohio State bought the contract out. For
OSU and UM, the risk (playing a BCS conference team outside their region) has to be worth the reward (the game must be on national TV).
Ohio State at Syracuse or UConn is as appealling on a national scale as Ohio State at Baylor or Ohio State Mississippi State.
It has nothing to do with the Big East's status as a conference, but the status of the teams in the conference.
Mike Tranghese, who I have a great deal of respect for, especially after he took the high road in the interview during the game last night, knows that the programs that he does have must invest money to get back to where the conference was five years ago. If WVU or Louisville have a 'home' venue that'll seat 85,000+, and there's an assurance they'll be a 10-win capable team 10 years from now, I think JT and Gene Smith would schedule them in a heartbeat.