I completely disagree. If my goal was to transverse the South Pole exactly I would be extremely careful to make sure I had done so. This is of course granting the idea that there are signs saying "South Pole that way".
But the explorers your referencing do not have the benefit of being you. They had no question in their mind that the earth was a globe. That's what they were taught. They followed the signs, they followed the path others before them have taken from one coastal antarctic port to the other. Compasses don't work there. Without a question that the earth is a globe and that they are truly circumnavigating Antarctica, and not a peninsula, they would have no need to be "extremely careful" to make sure that they had circumnavigated Antarctica to prove it was a continent.
There are a lot of assertions in here and zero support. Unless you are going to start citing sources for this it should just be ignored as biased editorializing.
Have you ever met someone who calls themselves an "explorer"? They are universally brainless thrill seekers with too much money on their hands. Scientists are not explorers. Scientists are poor, and need to work for a living. The only reason a scientist goes to explore a far off exotic location like Antarctica is if a government is funding it, and the governments of the world lost interest in exploring Antarctica pretty much after they sent the first explorers in the late 1800's/early 1900's. Today some government institutions merely send people down there to study wildlife in a single spot, then return. Thorough, investigative and fundamental inquiry of the Antarctic continent is not conducted.
Every single time someone goes down to Antarctica in a challenge to cross it they merely trace steps of the early explorers, overly prepared with warm luxuries and survival safeguards of a millionaire on vacation, with books and stories in their bags about Antarctica and the people who died there. These people are merely doing it to say that they crossed Antarctica.
I don't see anyone crossing Antarctica horizontally to those few vertical paths. A true explorer wouldn't pride himself on taking a path others have taken.
Where do compasses not work? Today we have GPS to know our location.
Compasses do not work where the magnetic field lines are vertical, which is a good chunk of the entire Antarctic circle.
GPS works by telling the receiver how far it is from the broadcasting device. The receiver knows that, under theory, every 69.5 is one degree. So, if a receiver is 347.5 miles from the receiver, the display takes the coordinates of the broadcasting device given to it in the stream and adds 347.5 miles to it to output a degree coordinate for the receiver's location. It is possible to use this method of navigation to avoid getting lost and assign coordinate values to all of the locations near that broadcasting device.
The same devices could be used on a plane perfectly well. The xy coordinates would simply be artificial constructs used to assign location names to the surface to navigate. In order to take those xy degree coordinates, which are designed assuming 360 degrees on a globe, and use it to say that the earth is a globe, which it is not, further investigation would be required beyond the simple act of navigating from point A to point B.