I'm saying that we shouldn't radiate if it would be expensive. It's not easy to force the heat out to the radiators; normally radiation only works because the radiator is more conductive than the rest of the system, and so it tends to pull heat from other components.
We can set up massive convection currents in datacenters on Earth, using air as a fluid. I live in Oregon, where we have a high desert region which enables the following pattern: pull in cold dry air, add water to cool it further and make it more conductive, let it fall into cold rows and rise out of hot rows, condition again to recover water and energy, and exhaust back out to the desert. Apple and Meta have these in Prineville and Google has a campus in The Dalles. If you do the same thing in space, then you end up with a section of looped pipe that has fairly hot convective fluid inside. What to do with it?
I'm merely suggesting that we can reuse that concentrated heat, at reduced efficiency (not breaking thermodynamics), rather than spending extra effort pumping it outside. NASA mentions fluid loops in this catalogue of cooling options for cubesats and I can explain exactly what I mean with Figure 7.13. Note the blue-green transition from "heat" to "heat exchanger"; that's a differential, and at the sorts of power requirements that a datacenter has, it may well be a significant amount of usable entropy.