> This is a one time cost.

Sure, until you need to replace or upgrade it. How long does a server on earth last for, how often does it need maintenance / replacing? And how long is the expected or desired lifetime for a server in space? Then calculate weight and cost etc.

> Maybe the running costs are cheap enough to offset this.

"Maybe" is hope, you can't build a business on hope / wishful thinking. And the running costs for data centers on earth can be reduced too if you build them the same way as a sattelite - solar panels + battery + radiative cooling gives you enough data to compare. But servers / data centers aren't built that way because of cost vs benefit.

> If achieving the cooling is only very hard and requires careful material engineering, then it can be worked out and they will get it done.

See, it's possible for sure - we HAVE computers in space, powered, cooled, running 24/7. The questions are whether it makes economic sense, both launch costs and running / maintenance costs. That's straight math, and the math isn't mathing.

> I suppose they could make something like the International Space Station, which would get regular traffic back-and-forth exchanging and servicing hardware as needed.

Sure, but the ISS itself cost ~100 billion to build and operate - probably more, this is based on a ten second search query. While I'm sure launches are cheaper than ever and will be even cheaper in the future, it's still tens of billions to build a data center in space, plus you'd need astronauts, supplies, hardware, etc - all a LOT more expensive than the equivalent processing power on earth.

> These are collective problems for the whole of humanity and will not concern an individual actor such as Elon Musk who wants to send more satellites into space.

True, so we as humanity should offer resistance to plans to launch thousands of objects into space unless they have a clear and definite benefit. I'm not worried about Starlink, it's a benefit to all the areas that don't have (open) access to the internet and they're in low-earth orbit so they'll fall back within 5 years. But I just don't see the benefit in putting datacenters in space, not when it's so much cheaper and more viable to put them on earth.