You can't set up shop in Antarctica because its forbidden by the antarctic treaty, which is backed by 32 Nations. If you think people wouldn't be conducting business there if given the option, you've somehow managed to overlook every other corner of the world where its not prohibited. Mining businesses. Tourism/adventure companies. Setting up stores, bars, and other entertainment venues to supply tourists and miners with things to do and stuff to buy. These are just a few things I can think of off the top of my head that would be happening in Antarctica if it weren't patently illegal.