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.
It probably increases Elon's share of the combined entity.
It delivers on a promise to investors that he will make money for them, even as the underlying businesses are lousy.
A Starlink satellite uses about 5K Watts of solar power. It needs to dissipate around that amount (+ the sun power on it) just to operate. There are around 10K starlink satellites already in orbit, which means that the Starlink constellation is already effectively equivalent to a 50 Mega-watt (in a rough, back of the envelope feasibility way).
Isn't 50MW already by itself equivalent to the energy consumption of a typical hyperscaler cloud?
Why is starlink possible and other computations are not? Starlink is also already financially viable. Wouldn't it also become significantly cheaper as we improve our orbital launch vehicles?
Distributing useful work over so many small objects is a very hard problem, and not even shown to be possible at useful scales for many of the things AI datacenters are doing today. And that's with direct cables - using wireless communication means even less bandwidth between nodes, more noise as the number of nodes grows, and significantly higher power use and complexity for the communication in the first place.
Building data centres in the middle of the sahara desert is still much better in pretty much every metric than in space, be it price, performance, maintainance, efficiency, ease of cooling, pollution/"trash" disposal etc. Even things like communication network connectivity would be easier, as at the amounts of money this constellation mesh would cost you could lay new fibre optic cables to build an entire new global network to anywhere on earth and have new trunk connections to every major hub.
There are advantages to being in space - normally around increased visibility for wireless signals, allowing great distances to be covered at (relatively) low bandwidth. But that comes at an extreme cost. Paying that cost for a use case that simply doesn't get much advantages from those benefits is nonsense.
Of course this doesn't solve the myriad problems, but it does put dissipation squarely in the category of "we've solved similar problems". I agree there's still no good reason to actually do this unless there's a use for all that compute out there in orbit, but that too is happening with immense growth and demand expected for increased pharmaceutical research and various manufacturing capabilities that require low/no gravity.
Imagine a liquid which can be electrically charged, and has a low boiling point.
(Ask 3M/DuPont/BASF/Bayer... - context 'immersion cooling')
Attach heat-pipes with that stuff to the chips as is common now, or go the direct route via substrate-embedded microfluidics, as is thought of at the moment.
Radiate the shit out of it by spraying it into the vacuum, dispersing into the finest mist with highest possible surface, funnel the frozen mist back in after some distance, by electrostatic and/or electromagnetic means. Repeat. Flow as you go.