I have rented many times in Chile. Prior to the first trip with a rental, I got one. I have never been asked to see it for rental purposes, on maybe 10 to 15 car rentals. It expired some time ago, and I almost got another one, just in case, but did not. The issue arises if you ever get pulled over by the Carabineros. Basically the IDL just translates your DL into other languages, with data inserted. (Chile has occasional checkpoints for valid ID/registration.)

I've never driven in Argentina.

From the "it couldn't hurt" department, it couldn't hurt to have one.