Why don't commercial flights fly over Antarctica?

While technically possible, risks like weather and visibility, and other factors refrain commercial flights from flying over Antarctica.
Smithsonian Magazine

A Century Ago, an Explorer and His Pilot Claimed to Be the First People to Fly Over the North Pole. Here’s Why Experts Doubt That Achievement

While the success of Richard Byrd and Floyd Bennett’s polar flight has been disputed, the former went on to accomplish ...
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Extreme flight in Antarctica

I boarded a Hi Fly A340 chartered for White Desert Antarctica (Tour Operator) to fly to the seventh continent; Antarctica. The flight time from Cape Town to Wolf’s Fang Runway in Antarctica is 5 hours ...