It's not illegal to go to the North Pole. It's just hard to get there. And when you arrive, there's not much to see except a lot of ice. The North Pole is in international waters (under all the ice).
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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.
Expect to pay between USD $30,000 and $40,000 for a two to three week cruise to the North Pole. Very few expedition cruise lines venture all the way to the North Pole, and very few vessels are capable and safe for such a epic journey.
Unlike the north polar region, which is preferred especially for flights between Asia and North America, it is not possible to come across passenger planes over Antarctica.