Space is a vacuum. i.e. The lack-of-a-thing that makes a thermos great at keeping your drink hot. A satellite is, if nothing else, a fantastic thermos. A data center in space would necessarily rely completely on cooling by radiation, unlike a terrestrial data center that can make use of convection and conduction. You can't just pipe heat out into the atmosphere or build a heat exchanger. You can't exchange heat with vacuum. You can only radiate heat into it.
Heat is going to limit the compute that can be done in a satellite data centre and radiative cooling solutions are going to massively increase weight. It makes far more sense to build data centers in the arctic.
Musk is up to something here. This could be another hyperloop (i.e. A distracting promise meant to sabotage competition). It could be a legal dodge. It could be a power grab. What it will not be is a useful source of computing power. Anyone who takes this venture seriously is probably going to be burned.
Specifically: Starship makes no economic sense. There simply isn’t any pre-existing demand for the kind of heavy lift capacity and cadence that Starship is designed to deliver. Nor is there anyone who isn’t currently launching heavy payloads to LEO but the only thing holding them back is that they need weekly launches because their use case demands a whole lot of heavy stuff in space on a tight schedule and that’s an all-or-nothing thing for them.
So nobody else has a reason to buy 50 Starship launches per year. And the planned Starlink satellites are already mostly in orbit. So what do you do? Just sell Starship to xAI, the same way he fixed Cybertruck’s demand problem by selling heaps of them to SpaceX.