These pictures highlight a root problem with this thread: definitions.
In this case, the definition of the word 'plane'.
The angle of the lower and upper arm, respective of each other, does not necessarily define a unique plane. If you take your upper and lower arm and fix them at 90 degrees to one another and rotate them through space around a fixed point, then they generate unique planes.
Imagine a bookcase with two long support beams and shelves at 90 degrees to said beams. Each shelf would therefore be considered a unique plane parallel to the other shelves and perpendicular to each beam.
If, for example, we defined our pool shot plane as the right foot, elbow, hand, and shoulder then imagine those four points on one of those shelves. If any of those four points no longer rests on that specific shelf then it is no longer in that plane.
My argument is that there's 1 plane (with a tolerance) for an optimal natural motion.
This theory defies the body's ability to accurately produce a variety of throwing motions. Even if we agreed that an optimal alignment between the forearm and upper arm does exist, it neither accounts for the necessary requirements to turn an arc into a horizontal vector nor is such a degree of exactness necessary for the body to execute said motion. The existence of an optimal does not guarantee the necessity of said precision.
The reason I led off with the mathematical principle is to highlight the problem with the one plane theory. Pick any throwing motion you like and twist the body to generate different planes (bending down for a shot, for instance). Any one of those discrete planes may or may not be optimal for pool performance, but they represent samples of the infinite planes that exist in the cylinder and sphere relationship.
So are other lines that a person's body can "naturally" takes to from the onset. I disagree that correctly aligning your dominant eye alone will necessarily lead to optimal alignment, if that's what you meant.
I said nothing about eye dominance. The generic 'correct position' need not be explicitly defined for our conversation.
There is a commonality that can be seen in almost all players who video tape their actions for the initial time in that there is usually a reaction of surprise in one or more facets of their form. Even experienced players who believe they have proper mechanics will often be shocked by some detail that they felt was one way but then find out it is another. In pool this can manifest itself as the upper arm and elbow protruding either toward the body or away, the lower arm not being vertical, the wrist curling, the grip.........etcetera, etcetera.
The reason I put eye/head placement in that sentence was due to the fact the head is a relatively fixed position on the human body. It's much easier to manipulate the arms, wrist, and fingers than it is to attempt to reposition the head around any arbitrary alignment of those parts.
If we define our optimal alignment by the position of those other parts, then we, by definition, must move the head to fit that alignment. If, however, we place the head first then we can take advantage of those infinite planes that exist in the cylinder and sphere relationship.
Take the example I described above. What makes each of those planes more or less optimal is not the relationship of the arms to one another (because we set that fixed to some arbitrary angle) but the ability for the eyes to gain the information necessary to process the shot. The head and eyes alone cannot define the optimal alignment as they are only one point in space, but the head does help dictate how the other motions of the body align and react.