The Spanish infantry were widely considered the best in Europe for some centuries; the Spanish themselves developed the tercio towards the end of the Reconquista (I presume deriving from the model of Swiss mercenaries) and thereby pioneered the style of warfare (pike and shot) that would displace and dominate throughout European militaries for the next few centuries. It was the capacity for effective combined arms formation warfare (as opposed to fighting as individuals or relying on cavalry) that paved the way for European successes in Asia (as with the decisive Austrian conquest of Hungary from the Ottomans in the late 17th century). The primary advantage that the European developed (in part by endlessly honing it against one another; bearing in mind that advantages of this sort dissipate more quickly when your foes are at near-parity in underlying social or physical infrastructure and can legibly dissect and copy what you are doing) and which persisted throughout their imperial operations was in logistical and tactical technology. In India, the British attained consistent battlefield success against local armies even when the latter had extensively purchased European technology and had the advantage of some mercenary European officers in addition to numerical parity or superiority. The tide of battle hinges heavily on morale and organization; low casualty numbers and minor setbacks can compound and escalate cooperatively as a result of mass psychology. The great innovation of Europe at the time was in developing and mastering techniques for coordinated formation warfare (not that this had not previously been discovered and lost in varying forms over the course of history).
Spanish supremacy in arms is generally agreed to have been finally and symbolically eclipsed at Rocroi in 1643; in the meantime, the Spanish had to contend with frequent, expensive conflict on multiple fronts against enemies who were not in remotely as much of a disadvantage in weapons and tactical technology (as well as massive naval undertakings against the Ottomans). European warfare during the Renaissance and Reformation tended to see the greatest of military powers paying enormous prices for modest gains at best, with the ultimate rewards being financial decrepitude...except for early imperial operations in Asia and America.
Moreover, the technological advantage of the Spanish was vastly greater than you claim. The Mesoamericans were sophisticated in some respects but entirely lacked metallurgy (or for that matter, domesticated draft and combat animals); obsidian shattered against Spanish and Portuegese steel. Notably, that steel was itself of notably high quality for the period; the ascendancy of the Saadi dynasty after Ksr al Kebir was in part attributed to the large number of Portuegese smiths taken as (particularly prized and well treated) slaves for the production of 'armas blancas' as well as Portuegese officers (therein lies another dramatic if more ill-fated example of long range imperial conquest, as the Morroccan army subsequently completed a dramatic trek across the Sahara and easily demolished the Songhai empire in an effort to secure the West African gold trade, but was unable to effectively consolidate such and saw profits dry up in regional anarchy instead). One should in the context of e.g. the Aztec conquest not underestimate the impact of even a small cohort of troops able to mount terrifying displays and manuevers (with gunpowder or horses) and shrug off blows from your melee weapons, especially when your army is already plague-ridden and demoralized (given the havoc already caused). Likewise, the diplomatic resettlement to Spanish hegemony was trivialized when both allies and enemies subsequently succumbed in enormous numbers to disease.
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Even after the disease took its toll, the Spaniards were vastly outnumbered by the Americans. Analogy: Suppose Coronavirus wipes out 90% of the world's population of asthmatic smoker 90+ yr old men. And suppose that also, the mathematics department at MIT produces more published theorems in 2021 than that entire demographic. The first fact is not the primary explanation for the second fact. Even if Coronavirus didn't happen and that demographic was not reduced by 90%, the MIT mathematics department still would have produced more published theorems. (And even if this last thing isn't true -- even if by some mathematical coincidence that 90% factor would make the difference -- it still wouldn't be fair to say that disease is the primary factor, it is clearly much less important than e.g. age, specialization, health, etc.)
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This simply underestimates the sort of devastating toll on organization and morale that even much more modest absolute casualty figures would have had. Much lower casualty rates can and will fatally disrupt social and military institutions (as with the collapse of Justinian's efforts to stabilize a broader Roman Empire with a mere 25% death rate); being the last coherent group standing in a sea of utter societal collapse would in fact be an overwhelming advantage for the Spanish even without any unique technological or organizational capabilities. It's not as if a 90% death rate is going to spare any coherent cadres beyond maybe a genetically lucky family or two. I would say the analogy here is not at all appropriate and in any case makes assumptions that are not at all definitively known to be true here (i.e. the controlled experiment has not been done- we know MIT professors outproduced xyz demographics in math papers in xyz years even without plague, we do not have a coherent case of a small band of late medieval Iberians laying the foundations for total continental hegemony in regions that didn't have the confounder of most of the population being disease-naive). Moreover, arguments as to the charisma and diplomatic acumen of individual leaders are to an extent appeals to a great man conception that while not essentially wrong must be acknowledged as inherently stochastic because they dependent on idiosyncratic personal capabilities of effective leaders- you are basically making an argument to sample bias whether you'd like to or not I would suggest. History is plenty affected by such but there were also Iberian new world expeditions that lead to little or nothing in terms of coherent gains (i.e. Ponce De Leon, who failed and perished in conflict with natives in attempting to establish a Spanish colony in Florida within a few decades of Cortez); if you want to refute that it'd take a careful catalog and analysis of every militarized new world expedition, not just the ones that became runaway successes.
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I think this is a big open question; currently I still disagree. For one thing, the initial plagues weren't 90% death rate, but more like 50% IIRC. For another... well, when I get to this part in the book I'll have a better sense of how disorganized they became. My guess is that you are way overestimating it. Remember, I'm not saying the effect was negligible--I'm saying the effect wasn't so big as to undermine the conclusions I drew about tech and diplomacy advantages. (Or the conclusions I list in the "lessons" section). You are the one making the extreme claim here, as far as I understand you currently."
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I have seen military historians cite that 25% casualty rates are generally enough for the total collapse of the viability of a military force. Near-indiscriminate loss of personnel randomly distributed across a social or military hierarchy- imagine a if a quarter of everyone you knew disappeared tomorrow- in a both direct functional and psychological sense would be utterly devastating. 50% is well over the threshold for total societal collapse; the Black Death killed "merely" 33-50% of the population across affected areas and very much brought contemporary society to its knees. When you have superiors, family, and comrades dropping left and right and others disabled by symptoms I really don't think your fighting readiness is going to be in a great place. Bear in mind that premodern warfare swung on morale collapse coincident with vastly lower absolute casualty rates, with most casualties inflicted during the rout. My claim is not in the slightest extreme; the calculus of life and death and any semblance of social cohesion being thrown out the window by plague is going to fundamentally wrack the afflicted society at every level.
In any case, the differentials between top rate and mediocre militaries at any given point except where extreme technological disparities apply is often more about discipline and coordination than it is about anything else; friends in the military involved in overseas training have noted that middle eastern militaries are hampered by very poor attendance and frequency of routine drills to the point where discipline is often a farce (even in supposedly 'elite' formations) while African militaries often have virtually no coherent structure beyond hurling a mass of man at an objective, and history is rife with examples of a seemingly mind boggling set of disciplinary and command failures on an elementary level costing battles and campaigns; human systems largely succeed in spite of their own catastrophic noisiness and dysfunction (From the Jaws of Victory by Charles Fair is a book thick with fun examples of this if you can find it) . A force fully synchronized and controlled seamlessly by AI would likely best modern militaries even at a technological disadvantage; a force or diplomatic initiative advised by such would only leverage a significant advantage so if the leadership was politically and psychologically capable of heeding good advice when it was delivered to them (and the nuances of personal diplomacy are probably the final frontier in respect to what one can have an AI parse and respond to). I mean in essence what you're saying is that given an utterly brilliant, ruthless, and calculating leader at the top end of the spectrum of human potential then North Korea- or xyz nation- could vastly outperform diplomatically and strategically. And sure, of course that would be the case; just look at how routinely the Greatest Power in the World (tm) has had insanely inept leadership over the past two decades and how much trouble that has caused, and how even mildly canny albeit already powerful operators with pretty transparent goals (Russia, China) have been able to take advantage of that. Our own understanding of complex systems on the human timescale, ( see e.g. the farcical efforts of the CIA to wrangle insights out of behavioral idiosyncrasies amongst the Soviet Politburo during the Cold War...or just the modern state of biomedicine and the most of the social sciences), tends to be woefully inadequate even at whatever is thought to be the contemporary 'cutting edge' ; anything that could actually deliver accurate, self-consistent predictive analysis thereof would be a gargantuan leap forward.
While tangential, this is notably the key failing point of much of military fantasy and military sci-fi where such things as AI robot armies or undead armies or whatever are concerned. An enemy that is seamlessly coordinated by a single will or indeed which is stupid and mindless but simply has no fear whatsoever of death will vastly outperform against larger and better equipped forces; men do not go into battle looking to die and even elite formations will withdraw rather than fight it out if outmanuevered (see e.g. the Silver Shields in every major battle Antiochus the Great lost; if this can be overcome even temporarily you can see things like e.g. the dramatic efficacy of the Theban Sacred Band during the Sacred Wars). Warfare, especially premodenr warfare, hinges a lot on barely tamed human psychology that is rather wired to not keep going if death seems a likely outcome; men go to war for plunder or defense of their assets, not to look the grim reaper in the face. This is also why assaults routinely failed in months long premodern sieges even when the besieger could leverage enormous numerical advantages; anything that can just keep walking knowingly into the jaws of death has an almost immeasurable advantage over a mere human being.