Chickens and many other birds appear to bob their heads because their eyes are fixed in their sockets, so they can’t fix their eyes on a point while moving, but instead have to keep their head still. What looks like bobbing is the bird pushing its head forward and keeping it completely still for a moment while its body catches up. Without keeping its head still, it wouldn’t be able to see much of anything very effectively, prey or predator.

T rex might have been able to move its eyes, in which case it probably wouldn’t have bobbed its head.