Moreover, if rains fell in such quantities over the course of these dynasties, they would have quite dissolved the mud-brick tombs of Sakkara, then in the process of construction and presumably not yet buried by the desert sands (no, I can’t prove this point).
Quoting Mark Lehner from Notes and Photographs on the West-Schoch Sphinx Hypothesis :
Perhaps this seems circular, but it is moot anyway if we don't know exactly which mud-brick tombs West and Schoch have in mind. The importance of this is that many of those tombs were only excavated between 1935 and 1956 by Walter Emery, who found that the superstructures of these tombs had been denuded to within a couple of meters above ground level, and sealed in the debris from the collapse of the walls already by the Third Dynasty. Smaller tombs of the Second and Third dynasties were built around and even on top of those of the First Dynasty. The interior chambers and compartments of the First Dynasty tombs were preserved because of the collapse of the superstructures, or because of sand and gravel fill put in by the builders. The whole cemetery was subsequently engulfed by sand. So West and Schoch might be looking at mudbrick that has only been exposed in the last fifty-nine to thirty-eight years In this case they did not even furnish a photograph of any mud brick tomb until the release of the unabridged version of their video "Mystery of the Sphinx." There we see West standing down inside what looks like the substructure - or one of the interior compartments - of a mud-brick mastaba and saying, "...these mud-brick walls are in relatively stable condition...." Which mud-brick walls? I invite Schoch to point out the specific mud-brick exposure he has in mind. Again, such an identification is possible because each of these tombs has a number. An easy reference is W. Helck's article on the archaic Sakkara necropolis in the Lexikon der Ägyptologie (edited by W. Helck and E. Otto), Volume 3, map on page 388. This may be quicker for Schoch and West than going through the volumes of W. Emery and J.E. Quibell,  but we would like, of course, to check the specific mud-brick exposures that Schoch refers to in those original excavation reports.
I recommend the complete article to be read to get a complete view of the thoughts of Mark Lehner.