All the comments are negative so I'll play the devil's advocate. Here's the steelman case for SpaceX orbital datacenters.
# EARTH IS FULL
It sounds ridiculous but the ability to build AI datacenters on Earth is nearly exhausted. The options are:
• USA, Australia. The electricity infrastructure has already bottlenecked and some datacenters like Colossus are being forced to build their own power plants, but that's also bottlenecked on gas turbine capacity. Hacks like recycling jet turbines only squeeze a bit more out. Terrestrial solar can't be used to escape this problem because you need the clusters to run at night too.
• Europe. Deindustrialized, EU Commission is anti AI, very expensive power, grid also bottlenecked. Forget it.
• Middle East. Had some datacenters until they got blown up by Iran.
• China. Got power but bottlenecked by trade sanctions. Might well do a big buildout when Ascend starts to be competitive, but Chinese demand is likely to absorb it.
• Latin America, Africa, south-east Asia, etc: bottlenecked by political stability, not pro-business enough, etc.
In space you don't need gas turbines because solar can be 24/7, political risks aren't there, you aren't bottlenecked by grid capacity. Even if it costs more to put stuff in space that doesn't matter if space is the only place you can put stuff.
# INFERENCE NOT TRAINING
Trying to do backpropagation in space would be a bad idea. You need extreme locality in a single physical location for networking reasons. But a lot of modern AI load including training load is just inference, which only requires small pods not entire clusters, and bandwidth needs in/out aren't that high. Inferencing can fit on a satellite.
Space radiation isn't necessarily a problem. Bit flips can be tolerate to quite a high degree for inferencing because models can recover from corruptions in the activation stream or even some bad tokens.
# COOLING
As the article lays out this isn't necessarily the problem people are assuming. Also there are candidate designs from decades ago for ferrofluid droplet radiators. These might be overkill but can in theory radiate huge amounts of heat without needing to launch big radiators.
# COST
Unlike terrestrial data centers which are always bespoke projects, inferencing satellites can be mass manufactured. SpaceX and Elon in general are good at setting up mass production lines, and it seems apparent that SpaceX has no intention of throwing very high margin Nvidia hardware into orbit. The plan is to use Tesla's AI chips i.e. SpaceX could acquire accelerators at cost. This changes the cost calculations quite a bit. Although these accelerators might not be useful for training or research, most training workloads would stay on Earth so that doesn't matter (the inferencing loads moved into space would free up terrestrial hardware for training anyway).
The real wild card is if there's enough demand for a 'good enough' model that it's predicted to last the lifetime of the satellite. In that case the weights could be fabbed directly into the chips like Taalas does, and so the energy consumption would be far lower.
# BUSINESS CASE
It's possible that datacenter construction goes the same way as nuclear and becomes impossibly expensive here on Earth. If so then SpaceX can end up with a near monopoly on new inferencing capacity, making them the gateway to AI and the new Nvidia.
What's especially confounding is that the mere existence of orbital inferencing might actually create that outcome, because politicians would find it much easier to squash datacenter / power projects to please activists if there is a genuine alternative!
Note: I'm not invested in SpaceX.