I guess that was before they realized they needed to explicitly write down the rule that a dog can't play basketball.

Joking aside, there has been plenty of individual periods of enlightenment where people would do what actually made sense instead of what the stupid rules made them have to do otherwise.

There were a few, most famously Hatchepsut in the 18th dynasty. One all the way back in the first dynasty would be news to me.

I think even by then the rule such as it was was in place. King/Pharaoh was as much a role to play as it was an office to serve, that role is "son/reincarnation of Amun." The theology didn't allow for the concept of a Queen Regnant; you didn't have to be a man to be King, but if you were going to be King, it meant you had to play a man on television. Men were almost always cast in that role.

Almost always. There were the occasional women who ruled as regent after her father or husband (or both's) death and until her son was old enough to rule on his own, and fewer still who genuinely held the rank of King. Then there was Her Majesty Hatchepsut The Exception, whose rise to power and rule was...unusual.

As far as I can tell, Amun was only 5th dynasty stuff at the earliest, and not even as the top dog, the 5th dynasty is barely the start of the sun cult with sun temples and the Osiris cult with the pyramid texts. 3rd dynasty Djoser is the first to start the whole "the king is a god / divine of body" concept, as far as we know. This here would be even before that, I don't know that we can claim there were royal roles defined as being the male incarnation of a top god, this here is 1st dynasty, that's a few centuries too early.

I'll grant you it's difficult to say with any certainty all the way at the other end of history. I'm not sure the complete sentence had been invented yet; Anything "written" about Narmer is more like Washington Crossing The Delaware than a history book, though he is heavily associated with Horus. The Narmer Palette depicts Horus delivering the personified land of Lower Egypt to Narmer as he smites an enemy, and on that basis I'm going to "some guy on the internet thinks" he at least had the concept of divine favor or mandate or something.

Before that you get "Apparently there was a guy who identified himself with a little doodle of a Scorpion? Probably played by Dwayne Johnson?"