I don’t understand how you can call it a certain improvement. As an aspiring historian, one thing that drives me crazy bout a lot of objectivist historians is the same trouble subjectivist and intrinscist historians have: lack of causality.
Both cultures were bad, because both suffered from the same self-sacrificing plague of mysticism. The conquitodors enslaved the aztecs and felt a duty to massacre them because of their dilusion of mystic significance. Yes, they were a more advanced society, and yes they had a greater respect for the key elements that make human advancement possible. But they did it with a bad philosophy. Evil must stand upon good to thrive. The evil of mysticim paired with the good of individual rights and advancement manifest itself in the early european settlers.
How can you condone coercion, even if it abolishes ignorance. The ends do not justify the means. Open trade would have been more rational.
PS: I know I said something bad about objectivist philosophers, don’t get upset. I’m not in anyway condeming the pholosophy, only a few people’s inability to be consistant. 
The Spaniards who conquered the Aztecs and Incas were soldiers left over from the campaigns to kick the muslims out of Spain. They acted as marauding armies, but they weren’t just a band of nomadic barbarians, they succeeded for various reasons demonstrating their own cultural superiority (even though the soldiers were probably the worst exemplars of it) and demonstrating the inferiority of those they conquered. In both the downfalls of the Aztecs and Incas, the tributary tribes were open to helping the invaders get rid of their native overlords. The Spanish soldiers passed on diseases to the people in the Americas because European cultures had long been domesticating aminals, where many deadly diseases orginate. Animal husbandry is an important part of civilization and the fact that many Indians had no immunity to these diseases demonstrated their backwardness. Also the Spaniards brought another implement of European modernism, guns, but with so few Spaniards these were more psychological than military.
Again I must refer back to the fact that many tribes flocked around Pizarro (Incas) and Cortez (Aztecs) to get rid of the two great empires of the Americas. Now the aftermath was a complete disaster as should be expected from the spread of diseases the Indians couldn’t combat and the fact that the soldiers were there for gold, silver, or land. However a true benefit from the overthrow of the Aztecs especially was the ending of human sacrifices to the sun, which were drawn as tributes from conquered tribes.
I think it is undeniable that the end result is preferable to how it was, but the means were messy, bloody, irrational, wrong, etc. But I defy anyone to show me a military conquest from the sixteenth century that fit any rational or Objectivist ideal, which is a contradiction in terms almost. We cannot judge historical actors in their own time because they didn’t come up with all sorts of ideas, the precursors of which didn’t exist. Aristotle had only been rediscovered by Europeans a few hundred year prior and the Renaissance was just beginning to reach its form. Had Ayn Rand been born at this time period I can guarantee she would not have been any life-altering philosopher for anyone, because too many things necessary for 1905 Russia to exist had not yet been developed or taken place.
In looking upon these events, we must judge them primarily by their ends. The means should also be discussed, and certainly if their were and Aztec Empire today we would deal with it differently than Cortez did, but this is an irrelevancy. What is important is how American (and subsequently Mexican) culture and civilazation was changed by the conquest, good and bad. And on the whole I think it was a net benefit.