I know this thread is a few weeks old, but the subject is directly related to my question, so I don't mean to hijack this thread, but since you're an air traffic controller (OP), maybe you can shed some light on what I'm missing here.
The flight path you just outlined above would not work on the flat earth map, obviously, without taking a huge detour. At least not with the current flat earth models. In fact, I believe that flight path is strong evidence (if not a proof) of a globe earth.
What I'm currently struggling to find an answer to is why it appears that there are no flights that go directly over Antarctica, despite the fact that in some cases a flight directly over Antarctica would be the shortest possible flight. If the flights do exist, I can't find any.
The most-obvious path for this example I think would be Western Australia to southeast South America. The largest international airports, if I'm not mistaken, in each of those continents are Perth, Australia (PER) and Buenos Aires, Argentina (EZE). If we search for a direct flight from PER to EZE, it would look like this, going directly over the center of Antarctica. This flight below, I believe is only theoretical since I could not find any actual flights like this. This flight, if it exists, would be about 7800 miles (6800 nautical miles) and last about 15.25 hours.
On a globe, it would be more-or-less like this.
The problem is, it seems no flights ever go over Antarctica this way. I tried searching for any flights that go from anywhere in Western Australia to anywhere in South America. All flights either go to South Africa first, or to Eastern Australia first before flying to South America. Some flights from Eastern Australia to South America do fly over Antarctica, but only the edges, which of course would still be possible on a flat earth map.
This doesn't prove that the earth if flat, obviously. But to me it just raises suspicion. Actually, if one could confirm that there are flights that take this route over the South Pole, it would prove that the earth is a globe, right? But I think the actual, defined polar routes (as in the image below, from Wiki) agree with the my search that no flights ever go over the center of Antarctica.
The flight path's shown above are possible on a flat earth map, although it would require you to essentially fly around the outer edge of the earth, which would not be the fastest route.
This problem does not exist on the North Pole, however. There are plenty of flights that regularly go right over the Arctic center and in fact. The flight from Los Angeles (LAX) to Dubai (DXB) takes this flight of 8300 miles (7200 nautical miles) and lasts over 16 hours.
And there are plenty of other "polar routes" that go right over the pole.
So the question is: Why? Why do no flights go over the center of Antarctica? It's suspicious that going over the North Pole is common, but going over the South Pole seems non-existent, and it seems unlikely that there would be no demand to fly directly from WA to South America. And if there are flights that do, why is the flat earth debate even a thing?