Same from my experience, keep bringing them dollars

wait until your rent and other prices drive up by influx of abnormal salaries for the local economy and everything becomes ultra-expensive for you. Barcelona, Mexico City, ...

Are those people planning to all stay on the same place? South America is quite big.

Anyway, I'm not sure rent is high on those place (or rater specifically Mexico City) because of immigration. I can't imagine deciding to move to Mexico and picking specifically Mexico City instead of somewhere else (it would be like deciding to go to Brazil and insisting on living in São Paulo - people have many reasons for living there, remote working immigrants have almost none). At the same time, there are plenty of reasons to have expensive rents there that don't depend on immigrants.