Fascinating read here Bruce and Will. Thanks for the insightful exchange.
I agree with will that the visual element is critical to putting success. As Bruce knows, I think that it is more complicated than just ability to see the line from a side-on position. I think that it goes to the player's vision itself. For instance, if a player is right eye and right hand dominant, they will tend to have a different approach than someone who is left eye and left hand dominant - assuming both are putting right handed. Now if you add visual irregularities to the mix it gets even more complicated.
I believe that putting well is a more athletic endeavor than it is often given credit for being. The fine motor skills that are used (feel, touch, distance control), the sense of your own body and how to get it into the optimal position for you to get the ball on line with your stroke, the sense of timing to control the distance and pace of the putter head and to square it through impact, all of these are very athletic skills. Then there is the intuition or judgement that plays in with how to adjust to slope, break, wind, mositure, grain, bright sun, flat light, temperature, impediments, ball marks, sand, etc...
IMO good putters are remarkably skilled people who have developed their talent through discovery and practice.