Some people might ask, why not just move closer to the bird with FX cam?? That way you get more details. Of course. But when shooting birds, can you move closer? Birds have safe distance. Once you get past that safety zone, it will fly away and there goes your picture. So the further away you can stay from the bird, the better chance you can get it more calm and stable. So the longer your reach, the better that is too.
DOF is also a good point you mentioned. Sometimes you want a deeper DOF. The only way you can do it is to drop aperture. But a crop cam gives you a deeper DOF (since you have to stand further back for the same FOV), without the need to drop aperture and sacrifice shutter speed.