Why Couldn't the Aztecs Turn Spanish Rivals Against Each Other?

Si Sheppard says the splits among conquistadors were personal rivalries inside one Spanish world, so the Aztecs could not use them to stay in power.

Dwarkesh Patel points to the larger force sent to arrest Cortés, and to Almagro, Pizarro's second-in-command, who came back angry about the spoils and besieged Cuzco. Spaniards fought each other while taking over a much larger empire. Sheppard's distinction is that those fights stayed inside a shared Castilian background. An outside crisis meant to pit them against each other would have failed, because a common enemy would have pulled them back together.

Native rivalries were older and ran between whole societies. After La Noche Triste, Moctezuma's brother and successor sent emissaries to the Tlaxcalans and the Tarascans, hoping for a common front against the outsiders. Younger Tlaxcalans thought about joining. The old men who still held power had been fighting the Aztecs for decades and still saw the Aztecs as the existential threat, so they refused. The Tarascans said the two peoples were enemies and always would be, and that an Aztec defeat would be no loss to them. Sheppard says local peoples could have played European powers against each other only if the English, the French, the Dutch, or the Ottomans had been colonizing that early. For the Aztecs and the Inca, the Spanish were the only outsiders they had met.