Aside from the onesim mentioned above, there is no carrier I am aware of in South America which covers all of those places without incurring roaming charges. Movistar is in all of those places, Claro may be as well, but when you register for the SIM, you incur roaming charges once you move to the next country. A few years ago, getting a SIM in each country would have been my recommendation, as they were easily purchased from any kiosko for small cash and no questions. Lately, anti-terrorism efforts have encouraged more documentation when purchasing SIM cards. Argentina in particular was a headache for me, since I didn't have a national ID card, I had to go their main office instead of one of their many branches.
Most US carriers have travel plans you can turn on and off which allow reduced roaming fees and small amounts of data for global ready devices. I think T-Mobile has a very generous international roaming plan. I've used Verizon and whenever I'm about to leave, I have them turn the travel plan on for a month. When I return, they turn it off. I think it's about
$30 depending on the tier. I use it as an emergency phone since texts and calls are still expensive and I almost always go through the process of getting a SIM wherever I go. (I actually have a framed collection which hangs on my office wall, they're neat little mementos.)
Basically, there are several okay solutions but surprisingly few great, affordable solutions. I hope this helps.