> but heat dissipation at scale in space is an insane engineering challenge, the tech to make giant radiators work doesn't exist yet, and even if it did it would extremely costly to develop and deploy

Different problem.

Cooling can be done in space, it's a normal problem; not easy, nothing in space is easy, but on the scale of space it is normal.

However, at the temperature you would run a chip at, a radiator you make for space will just work better, reject more heat, if you leave it on the ground.

We get convective cooling down here as well as radiative. At operational temperature, convection more than makes up for the atmosphere being a heat bath at ~20 C or whatever.

Everything is possible. Doesn't mean you should do it. You can also put datacenters on the sea floor in a nuclear submarine. That might be even easier.

But does it make sense to do it?

No.