I am in no position to argue with you, as you know much more about this than me. I was merely offering suggestions, given that the context of the items was funerary.
The problem is that the AE did not just represent doorways but rather an actual building of which actual palace facade buildings have been found.
Are you saying a building(s) have been found that show the exact façade? If so where? Got any pics?
Most of them (on sarcophagi) are all different in minor detail, some similar but others very different?
Those aren't figures
Oh! Sorry, what are they then?
Yes it looks (to our mind definitely) like a building. Which it seems, you consider attributes "kingship".
Are you arguing that all the other boxes are not kings coffins (i.e. Lesser status or different period?) Or are you suggesting that all such palace façade sarcophagus are contemporary with each other, in a specific period, or of specific ethnic background, when to be a king / ruler meant you got buried in a quasi palace stone box?
Or as others have noted we have no way of determining the age or era of any stone box, and especially given the focus is on Menkaure ( no tangible thing to examine) surely a mere examination of :
-The layout of the G3 "tombs" and the considerable add-ons that have happened progressively over time. (Special note of the six niche room)
-The clear signs of the pyramid being built over an original (two entrance, one blind, configuration)
-The remnant of the wooden Anthropoid coffin held in BM is very likely a later NK design.
- Clear signs the G3 "temples" are ancient and have been rebuilt refurbished many times.
That there is little basis to attribute the lost , or imagined, drawing of Menkaure's sarcophagus to any one person or time in particular, at all?
My biased interest in your thread , whilst very interested in the significance of the Mesopotamian "connection" was in part the fascination with the extremely muddled confused state of what is thought to be contemporary with "X" Dynasty especially 4th.