> Let's assume the original inspiration for serekh
> iconography was Sumer.
I think we are far past having to "assume".
> How do you see this
> actually unfolding. For example, let's say Butis,
> Tasians or Badaris traded with Urukis, visited
> each other's settlements etc.
The Buto-Maadi, Tasians and Badari all show various clear ties to the Levant and no doubt at least some were migrants from the Levant themselves. Though the Naqada share similarities with the Badari it is clear their cultural "tool kit" as it were was of a much higher order from its beginning suggesting they too came from "elsewhere" as their is no direct precedent found in any of the other previous cultures. While there is a conversation to be had regarding Levantine/Egyptian migrations/contacts by these earlier cultures the heart of the matter lies with the Naqada culture post 4000BC. And even then this story does not begin until c. 3500BC with the arrival of Elite tombs found at Hierakonpolis which begin to show the first clear signs of unmistakable Mesopotamian cultural influence, not Levantine, well beyond "casual trade" or "monkey see monkey do".
This isn't an "evolution" or mere "borrowings" as what is seen here on many levels is fundamentally different than anything that came before that for me goes without saying was the result of a small yet direct influx of Mesopotamian administration. This shift is beyond sudden "inspiration" nor is there precedent prior. It just is. From this point forward this transformation rapidly accelerates not just culturally but technologically eventually leading to the formation of Dynastic Egypt. So to answer your question it is at this point where I see this all unfolding.
> The former saw the
> architecture of Sumerian palaces and aimed to
> mimick this in their homeland.
As seen in the OP it is beyond "mimicking" as some features are literally identical, for example the crossed-axe motif. It is also not just the palace facade style or the building itself, but several other Mesopotamian cultural motifs and technologies that are also found as part and parcel of this period. Also, though I have bloviated many a time here, I don't think people realize how sophisticated the AE became directly beginning and following the Elite burials and Hierakonpolis which manifested in a relatively very short period of time which all lends to the idea this was a result of continued outside influence. Regardless, just for Egyptians to have wandered into Uruk, or other Mesopotamian cities of the time, would not be enough to go home and "replicate" what they saw.
This requires mastery of several trades and technologies, like making mud-brick, not the least of which architecture, engineering, and large scale project management. Unless they "studied abroad" and came home these things would not be possible without an influx of the originating culture.
> I presume similar
> buildings would have been erected by the Nile
> delta as per your photos.
It may have just been one building for all we know directly associated with the Thinite kings and capitol at Thinis. A recreation of what they saw elsewhere in Mesopotamia.
> Then, the crest evolved
> from these foreign and regional symbols, ie Horus
> cult from Upper Egypt and Delta meets Sumerian
> palace facade...so the crest is a composite of two
What really is "Horus"? Horus in the north and Set in the south. Of course they at some point were seen as gods but what were they originally? I would suggest they themselves began as symbols of two different ruling, possibly foreign, cultures.
> Presumably, as local architecture evolved, the
> foreign influence was side-lined.
I think the influence of the Mesopotamian Foreign Elite was a direct one that lasted for centuries until its collapse in the 2nd Dynasty. What followed is another story as well.
> I can think of an analogous example in Persepolis,
> where Lydian and Ionian column makers from Greece
> were "flown in" to help with construction on the
> Is this the scenario you imagined?
To some degree though I believe the early Elites and Pharoahs themselves were of Mesopotamian origin as well.