In Dec 2022 my DH and I did the Santiago to BA route (included Antartica). We stayed several nights in Santiago before heading to San Antonio to board the ship. We thoroughly enjoyed Santiago. We did a tour to the Andes which included a stop at a vineyard. To get to the ship, we took a private shuttle via Viator to SA. Original plan was to do a wine vineyard tour on the way to the ship. However, that fell through because no one else signed up. The tour operator refunded some of the tour price and changed it to a private shuttle to the ship. The shuttle picked us up at our hotel.
Due to winds, the Punta Arenas port was closed. We ended up spending more time in Ushuaia due to the missed port. We missed Port Stanley because of the wind as well.
We fly out of DFW, and almost exclusively on AA. I found that airfare from DFW to SCL was much less (both $-wise and miles redemption) than it was from BA(EZE) to DFW. We redeemed miles for Business Class to SCL and paid for Premium Economy from EZE to DFW. This December we are doing the Antartica cruise as round trip from BA. Airfare (miles or $) for DFW-EZE-DFW is quite high. I jumped on my flights at the 300 day mark, when AA releases it schedules. So far that has been the best pricing.
I would agree with the post that thought you would have more scenic cruising from Santiago to BA. Depending on how long you will be in Montevideo, you may be able to do a shore excursion to Punta del Este if you are interested.