You can't fly into a restricted area without permission from the controlling or using agency. If you have a reason to fly through restricted airspace, you can contact the controlling agency for approval ahead of time.
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Restricted areas often contain unusual and hazardous operations, like missile launches, air combat training, and artillery firing. You'll also find restricted areas over large military installations or other areas deemed necessary by the FAA/government.
Usually, the danger area is monitored by the responsible authorities who cease operations if unauthorised penetration occurs. However, it is the responsibility of pilots to avoid penetration of danger areas.
The short answer is, no, it's not illegal to fly over Antarctica. But there are practical considerations that make it challenging for regular airlines to navigate across the land. In many parts of Antarctica, there's limited or no infrastructure, no landing strips, and obviously no refuelling stations for planes.
Aerodynamic altitude: If a commercial airliner flies too high, it will encounter less dense air passing over the wings to create lift. This can cause the plane to stall and fall out of control. Depending on the weather conditions and aircraft weight, this can occur anywhere between 40,000 and 45,000 feet.
What is the longest flight in the world by distance? The longest flight in the world by distance is New York (JFK) to Singapore (SIN) on Singapore Airlines clocking in at 9,537 miles. What plane can fly the farthest in the world?