It seems the CEO of DL made some comments in 2018 that give some insight. He wanted all riff raff that is not a skyteam partner or otherwise aligned to DL out of T4. In that call he mentioned that AF is contractually bound to T1 (it was one of the JV partners that built/operate T1)
We built terminal 4 with a view that that would be a SkyTeam hub at JFK, that we’d be able to attract all of the SkyTeam partners in. However some of them have long standing commitments such as Air France to the terminal 1 facility, Korean is in terminal 1, and we’ve got to create space for them to move in. I talk to the Port a lot, I talk to Schipol who’s one of our partners in terminal 4, about how do we get some of the other carriers that are not in the SkyTeam out of terminal 4 to move more partners in.
..We’re eventually going to have to consolidate and move out of terminal 2 so we’re looking at building more space on the property in terminal 4 and expanding.. long long term I hope we get all our SkyTeam partners together.. I think it would give us a big competitive advantage.
JFK T1 is in the process of being completely rebuilt and will eventually occupy the space of T1 and the former T2 & T3:
https://www.anewjfk.com/projects/the-new-terminal-one/
Just like AMS Shipol operates T4, the MUC FMG will operate T1.