Will Latin American stay underpopulated for another century?

Think of how many people live in Asia, and how few, relatively speaking, live in Latin America.

Latin America has (mostly) beautiful weather, lots of natural resources, and attractive cultural amenities.  Mock the living standard all you wish but even Bolivia has higher per capita income than the much better publicized “Asian tiger” Vietnam.  The region simply isn’t that poor by global standards.

Crime is a problem but likely will fall, due to aging, better policing, and perhaps lead removal.

What does a Coasian bargain between parts of Asia and Latin America look like?  Will many Chinese and Indians end up in Ecuador and Honduras?

I would bet no, but still I wonder.  Often we overvalue the permanence of the status quo and the region has seen some major inward migrations in times past.