Consider something like the role of courage in military tactics. If you had some populations who were simply less courageous than others, you'd have a different baseline for stuff like, does a phalanx work? Is a phalanx even necessary?
Even a minute difference in something like this would change the mechanics of the formation. So stuff like Alexander's globe-spanning conquests would suddenly become impossible as he hit a different population regime where his tactics don't work anymore, or the Mongols would hit some barrier where they would start losing all their battles because people weren't reacting the way they should, etc.
In reality, of course, empires like the Roman one absolutely depended on the fact that the same social systems and techniques worked just as well in modern day scotland as they worked in modern day Iraq - a legionnaire was a legionnaire, whether they came from egypt or wales, and they could and were moved around and interchanged.
That doesn't mean there cannot be genetic variations on those attributes though. No two legionnaires had exactly the same size[1] but that didn't prevent building legions acting as a unit…
In fact, the whole purpose of the phalanx as a combat organization is to remove the weight of individual actions: you don't need “courage” (whatever that means[2]) to stand in a phalanx, because you're clumped up with every soldiers, and you have nowhere to flee (and btw those soldiers are your neighbors and relatives, so fleeing would destroy all your social life back home, putting an enormous social pressure on soldiers).
There has been an extremely long and celebrated history of different nations and peoples employing different military tactics and being known for different sets of skills in battle.
But aside from that, it seems like everything you wrote is pure conjecture and even if some of it was true, that absolutely does not prove a point about there being no genetic component to intellectual diversity.
Sure - the basic concept of a multi-ethnic social organization presupposes that ethnicity doesn't affect how you react on social conditions. In the 19th century and early 20th century, it became fashionable to say that only nations of one ethnicity could ever function. There are, however, many centuries of empires functioning with a myriad of ethnic and cultural groups living under the same law and administrative structure, and it works fine, because people are basically the same everywhere. If they weren't, it wouldn't.
P 1. A policy is a set of procedures a state employs to get a desired reaction from a population.
P 2. An empire is a state that employs some policies across its entire territory.
P 3. Multi-ethnic empires with strong cohesion have existed.
So if you take 1, and 3, you see that for both to be true, people have to have very standardized reactions to policies across ethnic 'lines'. I state it with certainty because it's obvious.
