I would have to disagree that the entire free world would have collapsed with the fall of the Suez Canal and even the entire Middle East to Germany. The oil would have been a boon to the Germans, but America could make up the loss easily. Convoys going around Africa would have been a problem, but not existential. For the spoils of Africa itself? Let's not forget that looking at paper maps gives false impressions about global events. Once you look at a globe, you will quickly realize that Germany had no chance, this side of heaven, to absorb vast parts of the African continent, let alone defend it.
The Italians you say? What about them? They could not hold water in a cup. They surely would not have suddenly found the material, manpower, and most importantly leadership, to hold such vast lands. What is more, they were logistically so unprepared for war that they could not move the short distance from the Libyan border to the Suez, when only 30,000 British troops stood before their quarter of a million. No, the Italians were not going to be much help. The Germans would have to hold the vast lands.
Winning in Africa and the Middle East, would have meant a much smaller concentration of force for Operation Barbarossa. It would have surely failed, just like its much stronger historical cousin did. Just sooner.