There's a lot of sci-fi about the wealthy bringing on an apocalypse so they can rule the world that comes out of it. Two examples on TV now are Fallout (from the video games, obviously) and Silo.

One thing that gives me some small level of comfort is that the billionaires who have the means to make that sort of thing happen don't want to live in bunkers or a radioactive wasteland afterwards. They have it pretty good on Earth as it is now. So there's only so bad things can get (I hope).

To your point, it does feel like we are bouldering towards major disruption, even the unravelling of the fabric of society, thanks to worsening inequality as well as the impacts of AI. In the coming decades we may well have a billion climate refugees. We may have large swathes of the population who have no productive outlet in a world that still requires you to have a job to live. And that could go south very, very quickly.

So I guess my point is that if things get so bad you need to put your AI DC in space to avoid the unwashed masses burning it down, I suspect we'll have far bigger problems long before that becomes an issue.