So like you said, I’m correct. The only issue with thermal radiation is $/kg of payload.

That's not what you said. You implied the only limiting factor is a reasonable payload that can be resolved by the current incremental improvements to rocket tech.

What I said is that even with massive improvements to rocket tech, it will still be a near impossibility to get as many AI (or even regular datacentre) satellites into space.

The other issue is that the thermal dissipation problem is not solved for such a large amount of heat in space. It's quite hard to dump large amounts of heat in space, and it needs to be done rapidly with computing. And the larger you make your dissipators the more you run into "how do I move that heat from the source and out towards the edge of the dissipators?" Because you need to utilize ALL of the dissipator if you want to keep your server parts cool. But moving that heat around a massive array is not trivial. If you're using a fluid and moving it with pumps, then now your adding even more heat with the pumps.

And then there's the issue with long term investment. These server components are going to be obsolete in a few years (and nevermind failures). And IIRC, they have plans to regularly de-orbit these things every number of years, which means even more launches at a regular basis to keep the swarm numbers constant.

And none of that matters in the face of the low earth orbit crowding issue that IS a massive problem.