That is not a fake argument, but real physics. Yes, you can design out X kw can be dissipated by this much radiators, but that adds an enormous quantity of mass, more than the solar panels that feed it.
If you are trying to generate a profit, every extra kg puts you further in the red. It still costs over $1000/kg of mass to get into orbit.
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.