Radiative cooling isn't as big of an impediment as people think. It's part of the reason why a desert that's 120F+ during the day gets so cold so fast unless there's cloud cover to radiate back.[1] IIUC correctly, the theoretical maximum is over 400 watts per square meter, and existing tech can achieve 80-90+% of that. It's an engineering challenge, but no more than creating reusable rockets. The real challenge is building a reliable convective system from the heat source to the radiating mechanism(s), and just the general problems of building a compact package for delivery that then unpacks and orients itself once in orbit. No new science is required, and you can pencil things out today the same way Musk did when penciling out the economics of building a reusable rocket.

Another way to think about it is whether orbiting data centers can be solar powered. Few people seem to think they can't. The amount of area you need to dissipate the incoming solar energy is approximately similar to what you need to capture it, so if you can do the later you can do the former.

Is it actually financially viable at all? And if so what fraction of data center build-out is sustainable at the increased marginal costs? I dunno. I agree there's probably some irrational exuberance involved in analyses. But don't underestimate the time value of money, marginal cost structures, and related financing and RoI dynamics.

[1] Convection effects are also involved, but that cuts both ways as the atmosphere is also radiating back at you, which is much less of a problem in space. A significant fraction of the net cooling is pure radiative.

No, but every day, armchair business analysts and people high on AI optimism expand the infinite frontier of blind faith and unfounded optimism in the future value of LLM infrastructure.