I get that vacuum is a really good insulator, which is why we use it to insulate our drinks bottles. So disposing of the heat is a problem.
Can't we use it, though? Like, I dunno, to take a really stupid example: boil water and run a turbine with the waste heat? Convert some of it back to electricity?
The problem is essentially that everything you do releases waste heat, so you either reject it, or everything continues to heat up until something breaks. Developing useful work from that heat only helps if it helps reject it, but it's more efficient to reject it immediately.
A better, more direct way to think about this might be to look at the Seebeck effect. If you have a giant radiator, you could put a Peltier module between it and you GPU cooling loop and generate a little electricity, but that would necessarily also create some waste heat, so you're better off cooling the GPU directly.
However there are workarounds. People are talking like the only radiator design is the one on the ISS. There are other ways to build radiators. It's all about surface area. One way is to heat up a liquid and then spray it openly into space on a level trajectory towards a collecting dish. Because the liquid is now lots of tiny droplets the surface area is huge, so they can radiate a lot of heat. You don't need a large amount of material as long as you can scoop up the droplets the other end of the "pipe" and avoid wasting too much. Maybe small amounts of loss are OK if you have an automated space robot that goes around docking with them and topping them up again.
I think I get it. If we could convert 100% of the waste heat into useful power, then all good. And that would get interesting because it would effectively become "free" compute - you'd put enough power into the system to start it, and then it could continue running on its own waste heat. A perpetual motion machine but for computing.
But we can't do that, because physics. Everything we could do to generate useful energy from waste heat also generates some waste heat that cannot be captured by that same process. So there will always be some waste heat that can't be converted to useful energy, which needs to be ejected or it accumulates and everything melts.