Benjamin de Haas published a study in the Journal of Vision in which he followed up his previous work on retinotopic priors in face perception. We are used to seeing eyes in the upper visual field and mouths in the lower visual field. His experiments suggest that this could explain at least some of the Thatcher illusion. This argues against a strict role of holistic processing in that illusion.
de Haas, B, & Schwarzkopf, DS (2018) Feature-location effects in the Thatcher illusion. Journal of Vision 18(4): 16.