The fact is our eyes (and brains) have an amazing ability to adjust to our surroundings, and to take in and process information while we are on the move. If they didn’t our species would have died off a long time ago.
When you spend as much time as I do around batting cages, one of the things you’re bound to hear is a coach telling a hitter about the importance of keeping his/her head steady. What the coach means by this is that you should set your body in a position, and then the head should stay there throughout the entire swing.
The rationale is that if the head is moving then the eyes are moving, and it’s too hard to see the ball that way.