Should also point out that hair, eye and skin color are very dependent on climactic conditions and it doesn't take millenia to change. Homer (circa 800 BCE) uses the stock phrase "the blond Hellenes" in the Iliad and
Odyssey because the "Greeks" (Hellenes) had just arrived in Greece a few hundred years earlier from (probably) southern Russia, where being blond didn't mean dead of sunstroke before you were 15. Within another 1000 years, the 'Mediterranean' swarthier skin, darker eye and hair color was predominent in Greece - but as near as Thrace only a mountain or three to the north, there was a high proportion of red and blond hair, because the central Balkans was a distinctly Non-Mediterranean sun-filled climate - as was most of Macedonia.
And specifically Egypt was not next to a blinding desert throughout its history. Up until about 3900 BCE, the 'Sahara' wasn't. That was when the African Humid Period ended, and before that north Africa right up to the Mediterranean coast was a grassy savannah, full of lakes, rivers, scattered forest, and lots of grazing land. When the area dried out a number of hunter-gatherer groups that had lived there disappeared, and undoubtedly some of them moved east into Egypt - there are both early groups already in Egypt (Merimde, Badarian, Fayim) and also new ones that show up after 3900 BCE (Amratian, Gerzean, Maadi).
One should not expect skin color and other adaptations that are appropriate today to have been present 3 - 4000 years ago under different conditions or before new populations had completely adapted to new or changing environments.