Wikipedia: "The Pitcairn government's attempts to attract migrants have been unsuccessful. Since 2013, some 700 make inquiries each year, but so far, not a single formal settlement application has been received."

It's never been important enough militarily for anybody to build an airport. It's mountainous, with no big flat areas, so that's a big earthmoving job. It's at least 1500 miles to anywhere, so a small bush STOL plane can't make the hop.

So who wants to spend $100 million on their post-apocalypse hideout?