No I don't agree at all, while I accept that artists and designers used classical geometric constructions for the last 2,500 years ... I have used them myself for the past 40 years now, I reject the idea that drawing random classical construction lines over some well known spontaneous photograph is of any use to anybody. I think you are selecting images that fit your theory then shoehorning them into it, rather than analysing what you see in them with an open mind.
I insist pi, phi, and root-2 come to us from Classical or Hellenistic Greece, although they, the Greeks, may well have called some of it Egyptian
I believe Henri was part of the avant garde, as seems clear from the from the historic record. He made his career in photography not in fine art or architecture why on earth would he have chosen to apply the cognitive geometry of Classical Theory in preference to the intuitive Gestalt Theory?
Arabesque means in the Arab style it is almost always applied to symmetrical design elements, tiles, filigree, carpets and the like.