This question was originally tagged cinema, so to a degree, the first part of your question isn't really on-topic for photography. But inasmuch as it intersects with photography:
As you indicated, rotating the camera about the entrance-pupil (a.k.a., 'no-parallax point'; a.k.a., 'nodal point') (but the latter is a misnomer), eliminates perspective or parallax shift. In photography, this is useful when stitching together several shots to make a wide panorama, because, assuming no motion in the scene between individual shots of the stitched pano, it's easiest to pick the overlap section and perform the stitching with minimal (ideally, zero) masking or adjustment.
But static shots, even wide panoramas, don't have anything to do with head movements. From a
cinema standpoint, it's merely an artistic choice few people will notice. Think about human physiology: our eyes are inset at the front of our skulls, far in front of the vertebral stack. Our heads rotate around the vertebrae, thus causing perspective shift and parallax in our vision. (This is of course, separate from, and in addition to the simultaneous parallax we have with binocular vision).
In my experience, most videographers or DOPs don't set up their cameras and pan heads to rotate around the lens's entrance pupil; they're usually set up to place the camera's center of mass over the rotation point. This is just to make camera movements faster and safer and easier to control. Much like photographers with long lenses mount them balanced on top of the ballhead or on photo gimbals; it's the most mass-neutral position.