Gotham War isn't about breaking up Batcat. Yeah DC and WB really what King was doing and likely they wanted to get as far away from his writing as possible but that not the reason why they'dpush everyone aside.
It's also nothing to do with Damian. I know a lot of fans are thinking that because Gunn is going to feature Damian then there'd be synergy.
Synergy comes after the movie's successful not before. Nothing happening with Damian is to do with Damian.
Again Gotham War predates Gunn's announcement.