A right-hander player who steps forward in the stance with their left foot--unless they really twist/rotate their neck over the line--will naturally have their left eye closer to the cue ball/object ball then their right eye. Glancing down at the cue stick gives a parallax view for many of these players.
The problem you describe may be seen by holding a knuckle under one eye then rotating your head as if stepping forward into the pool stance. The knuckle seems to move but doesn't, like an aimed cut shot.
The work needed to reconcile the converging lines of the eyes--and to account for the fact that the stick is on a different line--is to find the spot on your face that when held over the line makes a straight shot look STRAIGHT and then "be there" for all shots.
The great Tom Simpson explained it simply. A higher or lower stance moves the head laterally, not just vertically. Find the stance height where a perfectly straight shot looks straight, your "vision center". Stand your vision center over every shot!
For most right-handed players who use a fairly traditional stance (left foot ahead) their vision center lies between their nose and right eye. Putting their left eye/dominant eye over the cue stick would ruin their shot making and send them to a chiropractor for neck adjustments.
"Dominant eye" and "chin over stick" have some validity for some players but need to be contextualized.
This makes sense. And Tom Simpson is great!:thumbup: