They could, if only they were allowed to.
§ 121.161 Airplane limitations: Type of route.
(a) Except as provided in paragraph (e) of this section, unless
approved by the Administrator in accordance with Appendix P of this
part and authorized in the certificate holder's operations
specifications, no certificate holder may operate a
turbine-engine-powered airplane over a route that contains a point—
(1) Farther than a flying time from an Adequate Airport (at a
one-engine-inoperative cruise speed under standard conditions in still
air) of 60 minutes for a two-engine airplane or 180 minutes for a
passenger-carrying airplane with more than two engines;
(2) Within the North Polar Area; or
(3) Within the South Polar Area.
However, AC 120-42 contains a rationalle on minimum range operations, and explains that twin engine range restrictions started a long time ago, and that turbine engine technology is now so reliable that number of engines is not the limiting factor anymore. From 202 b.:
All long-range passenger-carrying airplanes, regardless of the number of engines, needed a viable diversion airport in the case of onboard fire, medical emergency, or catastrophic decompression. Ensuring availability of en route alternate airports, adequate fire fighting coverage at these airports, and fuel planning to account for depressurization are sound operational practices for all airplanes, including three- and four-engine airplanes.
And AC 120-42 202 mentions that it may be possible for airlines to cross the Antarctic region in the following circumstances:
c. Those areas not supported within 180-minute diversion authority tend to be routes over remote areas of the world that are uniquely challenging to the operation. These areas include the South Polar Region, a small section in the South Pacific, the southern South Atlantic Ocean between South America and Africa, the southern Indian Ocean and the North Polar area under certain winter weather conditions. The additional operational challenges of these routes are equally demanding of all airplanes, regardless of the number of engines, and include such issues as extremes in terrain and meteorology, as well as limited navigation and communications infrastructure. Support of a necessary diversion and subsequent recovery in such areas demands added training, expertise, and dedication from all certificate holders.
I could not find any direct flights from Australia to Buenos Aires, all go via New Zealand or further. And those flights would avoid the shaded areas on the map I would imagine.
This answer has looked at the flight path of a Qantas flight from Sydney to Santiago, which uses Tahiti as a diversion airport. A flight over Tahiti is much more northern: