Firstly, I worry that I am coming across as overconfident. I haven't researched these topics in great depth, and if someone could correct my broad model of history, I'd appreciate it- there's no better feeling than updating a mental model and letting things click into place in a clearer way.
10,000 years ago, Europe, Asia, and Africa were hunter-gatherer populations. Such cultures succeed by taking care of their environment so that the things they depend on remain. Cultural evolution isn't necessary there; biological evolution already optimizes for hunter-gatherer humans.
When you develop agriculture, circumstances change. The most profitable move for society at large is to eradicate nature in favor of farms. The wealth and abundance that results from that makes room for selfish individuals to fight for power. Societies develop kings and slaves at this point. The wealth can be grown by further replacing nature with roads, cities, and infrastructure. With selfish people in power, this is inevitable.
In the Americas, the Mayans had reached this point and had fallen, likely due to overindulgance in those benefits.
Incas had no slaves and no currency, so theirs was a unique culture that fits the opposing viewpoint. But they also had no writing system, had only really been around for 60 years before Columbus arrived, and still had an elite class, so my view is that they would have become homogenous with other societies that were successful. As far as I know, they weren't conservationists anyway.
Cultures move to positions that are resistant to change, easy to fall into, and that provide an advantage over competing cultures. That means centralized power, military dominance, and some benefits for those in charge. Cultures that don't meet these criteria either become those that do, or are conquered by those that do.
American Indians (I am told this is the preferred nomenclature) were increasingly competing between tribes, and the agricultural tribes were growing. Either they would have soon walked the path that everyone else in history has, or they would have been wiped out by the larger southern civilisations.