Do you have a source for there being no wheel in Egypt, Morocco, Ethiopia, the Sahel kingdoms, the Swahili Coast, etc? It would very much surprise me.

Calculations in Donald W. Engels' Alexander the Great and the Logistics of the Macedonian Army (1976) show that human carriers were just as efficient as animal transport. Human carriers remained very common in Asia and Africa up to the 20th century.

Wheels require roads that are expensive to build and maintain, a public investment that required major state or regal power - often absent in Africa. European medieval powers were unable/unwilling to maintain the Roman road system. Africa's climate makes those investments even more costly.

Finally, the real game changer is not land but water transport. Cheap transportation happens via water, and again, unfortunately, Africa is at a disadvantage due to its unruly rivers.