The biggest problem appears to be the slow diffusion of civilization southwards. Despite having potatoes domesticated right next door, and other suitable crops like quinoa, maize, other Andean crops in general, and cassava (for the northern parts of the area), the locals never developed much on their own and mostly ended up getting swept away by the Mapuche OTL.
If crops/cultural ideas diffused earlier could be a highly successful region though. In the La Plata basin, the locals could develop a strong river civilization. The best way would be getting maize there a millennia earlier and give it more time to evolve and diffuse. That way whoever's in the Uruguay/Buenos Aires area (call them the alt-Charrua for simplicity) will be able to adopt it. Then we need to get llamas to spread to the temperate lowlands, although I'm not sure if llamas or their close kin could thrive in Uruguay. Maybe they'd domesticate the rhea instead. Civilizations like this could spread all over the Pampas/southern end of the Chaco and perhaps carry on a thriving trade with the Andes and Amazon in rhea leather and yerba mate. This could maybe be comparable/evolve like an alt-Mississippian sort of culture.
South of them in Patagonia they'd grow less maize due to the climate and be more confined to river valleys, but grow potatoes and quinoa and most definitely herd llamas and alpacas in addition to rheas. Coastal groups may import a fishing/whaling culture from TTL's stronger sailing cultures of Tierra del Fuego/Chonos and settle the Falklands assuming the Fuegians don't get there first.
Outside of the La Plata basin it's likely civilization would be rather marginal (and a transition between TTL's larger civilization in central/southern Chile, the Andes, and La Plata) but still much larger and vibrant than OTL. It's likely in Patagonia and much of the Pampas it gets swept away by horse nomads, much as they dominated the more settled peoples of the Great Plains, but perhaps a long history of utilizing the llama and rhea would help them out.
Yeah I do not know where you got the idea that Patagonia was ideal farming land from. It is one of the coldest regions in the Americas.
It's like the Great Plains in many ways. There's no reason you can't have a sizable amount of people living around the rivers farming quinoa and potatoes (domesticated right next door in the Chiloe archipelago, although quinoa would need a cultivar adapted to the day length) or indeed maize and trading with llama herders who use the land unsuitable for farming. Same goes with the Pampas.