So is it a physics problem or an economic problem? Sounds to me like you are acknowledging that it is just an economic problem. If it cost $1/kg to get to orbit then this wouldn't be a problem, right? Just make a bigger radiator.
But if it's an economic argument, then you need to do the actual math. How big is the radiator? How low could the price to orbit go? How much can you charge per million tokens in 2030?
The reason this is a fake argument is because the validity depends on the math, and nobody advancing the "you can't cool stuff in space" argument is actually doing the math.
Okay any argument about why space is uniquely challenging is going to revolve around physics. Sure it's not literally physically impossible, but we need to explain to people why this is different from shipping the GPUs to Ohio.
If you want math then https://andrewmccalip.com/space-datacenters exists. The numbers are grim for orbital DC. Even if you drag the launch cost slider all the way to $1/kg (by the way this is literally sci-fi, per ChatGPT air freight of semiconductors from Taiwan to Ohio costs $9/kg and ocean/train freight costs a bit under $1/kg for a reasonable shipment so good luck with $1/kg to LEO this century) it is still more than twice as expensive as terrestrial DCs.
It's a fundamental physics problem. You need to have huge radiating surfaces.
A 1GW datacenter with chips operating at 100C (which is probably doable) will need a radiator that has a surface of one square _kilometer_, and this is with all the favorable assumptions. Realistically you'll need about 2x of that.
If you want your DCs to be on a 1000km orbit (for reasonable ping times), you'll be able to _resolve_ these satellites with a naked eye!
Sorry. But this idea is fundamentally unworkable.
The economics is constrained by physics. AI in space is not viable if it costs $1000/kg to launch to space. Starship promises to cut that down to $100/kg (more if you believe Elon, but most don't), but that's still not competitive.
Sure, things would be different if the cost was $1/kg, but short of somebody building a space elevator that's just not going to happen.