You are right about the bolded. They will collaborate - B1G, SEC, Fox, ESPN. It's in all their best interests.ESPN won't have power over the Big10. The Big10 would probably prefer Fox to own the playoff. My guess is the playoff will be split between a couple networks to maximize the rights fees.
Like I said, pretty doubtful the Big10/SEC will control all the elite players. Back in the 80's an undefeated BYU laid claim to National Champs behind a stud QB in Robbie Bosco.
All it would take is a stud QB like Trevor Laurence playing for a non BIG10/SEC team and the debate begins. Especially if the winner of the BIG10/SEC playoff is an underdog.
As far as a debate - if the guys printing the ink (ie Fox & ESPN) say their non-open championship is the *Real Champion* and the other conferences are lesser, you can't win that argument. And frankly, they will welcome the argument anyway as a) it drives interest and b) it gives them infinite opportunities to puff up their own setup.
I still think it will all separate into 2 divisions. Biggest brands and everybody else.