AE was simply and mostly an Afro-Asiatic civilization with Nilo-Saharan affinities, anyone who says otherwise is simply misinformed.
Nilo-Saharans and Cush*tics are the same people by the way, Cush*tics are just Nilo-Saharans with more "Caucasian" affinities. Cush*tic languages originate in Southern Egypt/North Sudan where after a while, pastoralist Cush*tic groups spread to the Horn & Eastern Africa in general. They dominated the place which was formally inhabited by hunter gatherer groups and Omotics. Later on Semitic (From Southern Arabia) came to the Horn and some former Cush*tic speakers (mostly Highland Cush*tic similar to Agew languages) switched to Semitic with not much of a genetic admixture from South Arabians (It was mostly just a language shift). By the way, the Cush*tic continuum still exists to this day beginning from where the Languages originally spread (Northern Sudan/Southern Egypt). It starts with groups like Beja in the Red sea region of Sudan and Southern Egypt all the way to Eritrea (Beja, Saho, Afar, Bilen), Ethiopia (too long to list all), Somalia (Somalis) and Northern Kenya.
I suspect that there were probably a number of other Afro-Asiatic languages like Beja spoken in the Sudan which probably disappeared with the Arabiziation of the place.