I always thought this was a specious argument and that despite a lot of social media threads and Elon ravings, no one is really taking it seriously. The reason I think this is because no one ever brings up the idea of having a self-sufficient colony in Antarctica.
I mean to build a proper threat model you need to understand exactly what threats you're trying to mitigate I guess. But let's say it's the usual doom and gloom stuff, a) climate change, b) nuclear war/winter, c) meteor strike.
If anything an Antarctic colony stands to benefit from climate change. A nuclear war is scarier, but none of the fallout is going to reach the South Pole, and to be self-sufficient you had to solve your energy needs without much sunlight anyway (there are surely tons of undiscovered hydrocarbons down there waiting to be dug up and refined).
A meteor strike, well as long as it doesn't land on the colony, the problems are similar to nuclear winter.
So if you want to have a "backup" for the human race - the Antarctic Plateau is sufficiently remote, and about 10,000x easier than anything off-world.
But we don't even talk about it because everyone knows life on Antarctica is pretty depressing and PEOPLE JUST WANT TO DO SCI-FI IN SPACE.