A quick note to anyone actually wanting to visit Argentina on this fare: AAdvantage miles go a long way intra-Argentina, specifically 6,000 AAdvantage miles plus de minimis taxes gets you anywhere in the country on LATAM. (one-way). Check for availability on ba.com or latam.com. (AR tickets are also available, using ST mileage).
As the ex-CAI fares discussed above are mileage fares, and LATAM only has Y cabins domestically, my advice is that one is probably much better off not "wasting" unrestricted J mileage on this internal travel when such an inexpensive alternative is often available. LATAM redemption availability is notoriously funky/chaotic, but ime, it most decidedly does exist.