And native numbers shrank because they were subjugated, enslaved, and killed off en masse on top of the disease. Without the aforementioned three, the disease death toll would have bounced back within two or three generations if it goes right for them.
And if you actually LOOKED at HOW the Spanish conquered the Maya and the Inca, you would see that it was absolutely impossible for them to do so without the considerable help they had from native allies. If the conquistadors didn't have these allies, there would be no subjugation, no enslavement, and no massacres. Not to mention the fact that European style armies can't work affectively in the Andes, especially against native tactics in those mountains.
I never said that the Spanish weren't dependant on aid from native allies at times, but the fact of the matter is that they weren't always dependant on them, especially longer after initial contact, when native population had dropped and their societies were collapsing as a result of the epidemics. Without those allies, the conquistadors fail in their initial attempts, definitely, but the lower the population level drops, and the more native society collapses as a result, the easier it will be for the Spanish and others to carve out empires without significant aid. The Spanish technological advantage may not have been enough to defeat the Aztecs in situations where they were outnumbered thirty times over, but they did have a very real and significant advantage in combat, and post epidemic native society can't call forth the same incredible numbers the Aztecs did. Of course, there would still likely be a fair number of people willing to ally with European invaders anyways, so it really doesn't matter much whether the Spanish would ever be able to take control without native allies, but I believe they could have done so nonetheless.
I actually argued that the Andes would be a potential vehicle for salvation for the Inca, so I don't get why you are directing the comment about European armies having difficulty there at me.
I feel you are overestimating a population's ability to rebound from such a string of epidemics, and also ignoring the subjugation, enslavement, and mass killing that will likely occur among the natives themselves. Note that "European diseases" isn't one single plague that will sweep through once and be done with it. If the natives manage to survive an invasion and the diseases it brought with it, there is still the very real chance that the next invading force (or even a peaceful expedition, such as merchants or missionaries) will bring a new epidemic that they have yet to become immune to. Depending on how evenly dispersed the introduction of the major diseases is, it could keep the native population from even beginning to recover for centuries, and that is totally ignoring fighting among the natives and drastically reduced agricultural output from having so many less people tilling the soil for generations.