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.
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.
But are you sure that $100/kg is not competitive? I don't remember all the math, but even their initial AI1 design[1] would throw a lot of profit, if you can sell at the price they offered to Anthropic.
I suspect the price of manufacturing the satellite, plus chips, is the dominating factor, not necessarily the launch costs.
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.
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.
Deploy 4,000 and you're at 1 GW. That's 160 launches.
BTW: SpaceX has already manufactured and launched 10,000 Starlink satellites and Falcon 9 launches about 150 times per year. None of this seems unworkable.
Look at the numbers. 1kW of nuclear power capacity on Earth is around $2000, and that's 24/7 guaranteed power. So a 250kW cluster needs $500000 to cover its power demand with near 100% reliability and with some ongoing cost.
And if we're OK with some interruptions, then we can use solar+wind at around $100000 and with essentially no ongoing cost. If we assume the absolutely best projected launch cost of $100 per kg (vs the current one of ~$800), that's just 1 ton of material in space!
So you're off by 2-3 orders of magnitude in cost. And this kind of "it's unprofitable" is actually a fundamental issue.