A Critique of Notional Geometry in Painting Composition

I've always been suspicious of the idea that great artists of the past deliberately routinely used Pythagorean/sacred geometry underlining the compositions of their paintings. I've been reading on this subject in the excellent 'Classical Painting Atelier', by the excellent realist painter Juliette Aristides. She wrote about how the natural harmonious points can be established by drawing lines dissecting a rectangle, making the pattern or 'armature' pictured above. The pattern finds the divides the plane up into half, thirds and quarters, and these divides are the visual equivalent, supposedly, of the perfect pitches of the musical scale. She went on to show how various key features of Velazques' Las Meninas, (and other paintings by Raphael, Vermeer and Ribera) were defined by these lines and dissection points. Still I was left with the slight suspicion that there may be little more than co-incidence to these correlations. I noticed that plenty of other significant features of the given works bore no obvious relationship to the diagonal lines and intersection points, and those that do could be the result of unconscious judgement or co-incidence. (One remembers the nonsense about the supposed 'Bible Code', and how it was shown up as nothing more than random chance). To test this suspicion, I decided to apply the armature to my own paintings, which I know result from no geometrical pre-planning. The first one I tested was my Amarna Princess. Various key points are defined by the armature. Various key features are contained within the diagonals, in precisely as Aristides described concerning the Old Masterpieces she discussed. Similarly with my Red Dragon piece. (The bottom of the circle sits 1/4 of the canvas height from the bottom, and various other key points line up, none of which was planned). Similarly with the Centaur, where the diagonals appear to define many of the important lines and boundaries within the painting.