Lesson learned today, don't post stuff half asleep while binging GoT. As to the comment on population, that I can't say as to what the population was. Do you have sources on estimates around that time? Per wiki, during the boom under Amasis II some of their cities had populations of 20,000. Now not all are going to be in the military but that's a population to draw upon. Likewise, Pharaohs of the time were still encouraging Greek traders and settlers to come to Egypt.
Being half asleep is not too bad (I'm half asleep most of the time courtesy of my dog) but GoT definitely can be quite destructive to person's mind (the book was driving me nuts because I was simply incapable to memorize all personages and their relations).
"Population" at that time was not necessarily directly mapping into the army size and quality and AFAIK Egypt extensively used the foreign mercenaries, probably because they were more warlike than the Egyptian peasants (similarly, why would the Late Roman Empire with its huge population hiring relatively small bands of the Germans and whoever else?). I'm not sure how the "native" army of Egypt was formed but I doubt that they had an universal conscription or even recruiting based upon a certain percentage of population. Then, of course, goes a pure logistics: you need to maintain a permanent garrison of the wall and to keep some strategic reserve reasonably close.
BTW, building the wall against danger from the East is fine but how about the resources needed to defend the Western and Southern borders?
However, the whole idea is quite interesting because an idea of building a fortified line along the border or to defend some communications existed for a very long period of time and had been implemented in the various times and places (including those mentioned in GoT) with a rather questionable record in the terms of success. But in the region you are talking about the idea was seemingly "not there" and the question is why.