Why do you think Fox and ESPN are working together in any degree? The CFP awarded the entire playoff to ESPN who sublet some games to TNT. Do you think Fox just didn't want a piece of that pie?
ESPN tied their cart to the SEC and Fox tied theirs to the Big 10. If bringing in FSU/Clemson to the SEC brings in more eyes to ESPN, why would Fox be happy about that? College football advertisers pay more to air on the network which gets the highest ratings.
To me, the only level of cooperation shown to date was the SEC & Big 10 realizing they are the 800 pound gorillas in the room and telling the rest of college football "tilt this playoff to our advantage or we're taking our ball and going elsewhere". Other than that, these networks played divide and conquer and the conferences fell right into it.
If the P5 would have looked at the long view and worked together regarding TV, they could have followed the NFL's broadcast model, had more control of their product as a whole, and had much more stability. Opportunity lost, oh well.
At least the CFP finally had ESPN agree to air the championship game on ABC in 2026 and onward - hard to believe the 2nd most popular sport's championship has been held on cable for 15 years now. One other suggestion - with the NFL running its regular season into the 1st week of January now, hold the championship game on the Saturday of that weekend instead of on Monday. Make it into a College Super Saturday like the NFL's Super Sunday.