To that end, a small data center space isn’t about unit-economics, it’s a bigger mission. So the question we should consider is what can we put into space the further that mission. Can we put a meaningful sum of human knowledge out there for preservation? It sounds like “yes,” even if we can’t train ChatGPT models out there yet.
Datacenters in space have a lifespan measured in years. Single-digit years. Communicating with such an installation requires relatively advanced technology. In an extinction level crisis, there will be extremely little chance of finding someone with the equipment, expertise, and power to download bulk data. And don't forget that you have less than a decade to access this data before the constellation either fails or deorbits.
Meanwhile people who actually care about preserving knowledge in a doomsday crisis have created film reels containing a dump of GitHub and enough preamble that civilizations in the far future can reconstruct an x86 machine from scratch. These are buried under glaciers on earth.
We've also launched (something like) a microfilm dump of knowledge to the moon which can be recovered and read manually any time within the next several hundred or thousand years.
Datacenters in space don't solve any of the problems posed because they simply will not last long enough.