but should have. Makes sense.
No, it shouldn't. And it will make NO sense if it did.
As explained in the manual, in the PaintKit documentation, and so many times on the forum, it's just wrong the GROUND crew would have any relationship with the airline you are flying. The ground crew is a service offered and related to the AIRPORT so, it's obviously related to the airport only.
If the livery you are flying affected the ground operator, it would result in the absurd situation of having your own airline crew following you everywhere you go "just" because that parking spot might have your airline assigned to (because your airline is supposed to park there), but that doesn't mean they have a local presence on that airport!
The livery you are flying, instead, affects the logos on the ULD containers. And this is also correct, so you won't end up seeing containers from one operator when you depart, and *different* containers when landing, because on the landing airport the operators might be different. So the airline you are flying, correctly affect the ULD containers ONLY.