The idea of developing more independent nations in the region that would have stood up to the Axis powers' consolidation might have been one reason why Arab nationalists and nations could have found alignment with the Allied forces. The perception was that the Axis powers were looking to unify and consolidate nations under their banner, and an argument could have been made that there was little to indicate that Hitler would have been supportive of Arab nationalism. Given his disdain for religion, many Arabs who worshipped Islam might have also been threatened, helping to facilitate a move to the side of the Allies. While the Alliies might have sought the support of Arab nationalists, the post war implications would have been rather drastic in that other nations' that flew under the Colonial flag would have also demanded their independence. Supporting Arab nationalists would have signaled the end of British and French worldwide colonialism, something that ended up happening in any event as national sovereignty triumphed in World War II.
Nowadays, we think of the Middle East for oil, oil, oil. But back then, oil had not even been found in Saudi Arabia. The major reason why the British wanted the Arabs to rise up was because of shipping lanes and India.
The British Empire depended a great deal on its trade with India. That trade went through the Suez Canal, which was next to Egypt. A Central Powers presence in this area could threaten the Suez. So the British wanted the Arabs to rise up against the Ottoman Empire. They believed that this would strengthen their position and help keep the Suez Canal safe.