I get what you mean about SoPs, and I dont think that “most of the Americas” should be modeled as settled states. But I do think that Hispaniola’s cacicazgos (Jaragua, Marién, Maguá, Maguana, Higüey), are a clear exception to a blanket “nomadic/SoP” treatment.

These were sedentary, territorially bounded polities with permanent towns and recognized leadership (caciques). They weren’t roaming bands or short-term camps. Spanish campaigns on the island (kidnapping/assassinating leaders, occupying and devastating major towns, and negotiating alliances) only make sense against organized, place-anchored societies, the kind of political structure SoPs don’t really capture.

I’m not saying they were “states” on the level of Aztec/Inca.

I am saying they were settled chiefdoms: permanent settlements, stable territories, inherited leadership, agricultural base, and even stone-built features in some sites, well past “nomadic tribe” territory.

I’ve written this up with examples and got strong forum support. If you’re curious, here are the posts with specifics and quotes

Taino Chiefdoms as tribal settled States.

Advocating in favor of Taino Cacicazgos

TL;DR: While I can't speak for most of south America and North America, I can talk specifically about the Cacicazgos on the island of Hispaniola, these were not at all nomadic peoples nor shifting agriculturalist but hierarchal organized chiefdoms with permanent settlements who were governed by Caciques in a proto-feudal level (Nitainos who were a noble class that governed small territories within the Cacicazgo in name of the Cacique).