I feel GGG does not move his head because it will effect his punching power. I am sure he has considered moving his head but probably gave up on the idea because he wanted to stay balanced to throw his power punches. GGG has a good chin and does not mark up either, so why move the head.

Yes GGG did get caught and had his hands up to block the punches. So what? He is going to get hit, this is boxing. The punches probably did not hurt him either.