>> But military histories of the conquest support the assertion that the small parties of Spanish soldiers were able to defeat much larger Native armies thanks primarily to their superior steel weapons and organizational capacity, in line with Diamond’s argument.
I don't have a bone to pick with Diamond, but this widely disseminated narrative lacks nuance. When people say that a few Spaniards conquered the largest Mesoamerican empires, at least when it comes to Mexico and the Aztecs, they are forgetting an important detail. When the ragtag band of mercenaries and adventurers following Hernán Cortés arrived at Mexico, they landed smack in the middle of a long-running regional war between the "Aztecs", i.e. the people of Tenochtitlan, and, basically, everyone else in the area. And of course, in the typical fashion of foreign invaders, the Spaniards immediately became fast allies with the enemies of Tehnochtitlan as the dominant power [1].
Thus, every time the Conquistadores fought the armies of Tenochtitlan, besides their guns, germs, and steel, and horses [3], they had with them thousands of allied local warriors, mainly from Tlaxcala, if I remember correctly, at least enough to stand up to the numbers of the Aztecs' armies [2].
Note that towards the end of the campaign, Tlaxcalla and the other kingdoms were indeed devastated by smallpox. But the same disaster was suffered by the people of Tenochtitlan, also. The Spaniards really were the plague [4].
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[1] This is a story that has played out many times in history. For instance, when the Crusaders landed in the Holy Land, they immediately found themselves enmeshed in the constant churn of alliances and wars in the Middle East. Half of the time, half of the locals tried to kill them and the other half they tried to get them to help them kill the other half. The same thing happened in Iraq, when the US invaded. It is a story as old as invasion.
[2] In much the same way, when the Spartans held Thermopylae, until that dog Efialtes, gave them to the Persians, the 300 were not, well, 300; more like 7000, at least at the start of the battle. Even in their famous last stand the 300 Spartans were accompanied by 700 Thespians and 400 Thebans. The rest of the 7000 left to fight another day. Not that it would have made any difference anyway, not against the fully might of the Persian empire. Remember Leonida's apocryphal quip: when he was told that the Persians' arrows would be so many that they would darken the sun, Leonidas said "good, we'll be fighting in the shade".
[3] And La Malinche, a formidable woman who acted as their interpreter and go-between, and was probably a main reason the Spaniards managed to ally themselves to the locals in the first place.
[4] My source in all this is the Historia verdadera de la conquista de la Nueva España by Bernal Díaz del Castillo who was there and saw it all with his own eyes, so god be his witness. My source for the Crusades is "Les croisades vue par les Arabes" by Amin Maalouf.