So this video from the Natural History Museum:
https://www.youtube.com/watch?v=PUwmA3Q0_OE&t=37s
Shows population density over time.
China and India have high population density, for reasons that have been answered before on this subreddit before, with answers such as rice farming by u/darwinfish86 and rice farming and historical river valley populations by u/MiyegomboBayartsogt. (Japan similarly has high density relative to its land mass once they pick up rice farming).
Alright, so in my mind, farming, crop yield, and historically large populations lead to large populations in the future. But the fertile crescent has most of that (minus rice). Two+ historical river valley civilizations. Good farming even during the Roman era (at least I remember reading somewhere that the late Roman empire used Egypt for a significant portion of its food production).
And yet, if this video is correct, Egypt and the fertile crescent have lower population, and possibly similar or lower population density than parts of Europe both during Roman control, and after the area was no longer controlled by the Romans. Is this accurate? If so, why?
The numbers for the Roman empire are on the very low end. Chances are that every dot around 150 A.D could be doubled, and that it is more reasonable that there were 88 million Romans, than the 44 shown. Many historians have written about this, and often they do it from a local perspective. There are therefore a huge number of historians that have been thinking about this. Fairly common is that they think the Roman empire had about 60 million inhabitants during the reign of Augustus, and perhaps 75 around 160 A.D.
For a discussion about this, a suggestion is the book "the Fate of Rome", by Kyle Harper.
If we are talking about density and economical power, Egypt had a very high density, and a very well developed economy. What you must do is to ignore the desert. Those 5 million humans you see, all lived on the tiny stretches of very fertile lands irrigated by the Nile.
For a discussion of medieval Egypt, there is the book "Framing the early middle ages" by Chris Wickham. It will give you a totally different view of Egypt, one where it stands out as an economical centre.