The thing is with Chauvel was his (and others) roles were played down by the propagandists and anti French elements in the Foreign Orifice to enhance to appearance of the Arab Uprising breaking and defeating the Ottoman Empire. Having Arab self rule (in the opinion of Arabists) strengthened Britain's hand in the Middle East and weakened France, critically providing the UK greater control over the oil in the region, admitting the truth, i.e. the Arabs did very little of the fighting and that Laurance of Arabia was a delusional, melodramic, nut case would have revealed that most of the fighting and almost all of the success was down to the predominantly infantry, predominantly English allied force out of Egypt.
Where Chauvel excelled was in leading what was apparently the largest cavalry (mounted) force ever assembled and effectively deploying it against a seasoned enemy in their home territory. The Middle East was seen as a side show by London so didn't get many of the resources it required, i.e. Chauvel always wanted more aircraft, armoured cars and tanks, he was very keen on motor lorries too. He effectively employed the limited aviation and armoured support he did have. Post Beersheba he issued swords to the Light Horse and employed them in highly successful manoeuvre warfare, bypassing, encircling and cutting off enemy forces. He also negotiated surrender terms where the Turks would keep their weapons to defend themselves from our Arab "allies", on occasion, Light Horse Units would actually deploy in defensive positions around the Turks to keep our "allies" from butchering them. Damascus, famously captured by the Arabs had actually already surrendered to the 10th Light Horse Regiment as it passed through the city pursuing the retreating Turks, the battle had already been won before Feisals army got there, the rest is politics.