We also know they had negligible genetic impact.
> while these folks were clearly a tiny minority and their distinctive appearance was often remarked upon, this did not hurt their social standing in any sense; there was even a well-known Egyptian dynasty of "Black" pharaohs.
You say that like social standing determines who gets to be king. The Nubian pharaohs got their position in the standard way, by conquering Egypt. They weren't native, they took very little interest in their new territory, and they didn't last very long.
There was a well-known Chinese dynasty of Mongol emperors. What do you think the social standing of Mongols in China was before and after that happened?
Absolutely not. They were gone a hundred years before the beginning of Persia.