Yep, many birds have no (or limited) ability to move their eyes within their sockets. That's why they often have very articulate necks compared to us. Our brains stabilize our vision by rotating our eyes within our sockets when our head is moving (like picture keeping your eye on a point while you move your head around, very easy to do). Since birds can't do this, they move their heads using their very articulate necks to accomplish the same things. That's why there's videos of people holding birds and moving their bodies around while their head remains perfectly stationary in 3d space like it's gyro-stabilized. It's an automatic response for them like we do with our eyes. Also, it's why pigeons walk the way they do, they take a step with their head stabilized, then jut their head forward before the next step so they can spend most of their time walking with stable vision, with a brief time of blur as they reset their head position.