I am quite certain that you are drastically underestimating the scope of the problem of "getting rid of heat" when you're dealing with the discussed levels of power production.
Maybe, but that's a "simple" resource problem. The Earth radiates 20x more heat than that today, and it has not been optimized for purpose. Remember that the initial assumptions were that AI has already designed and manufactured tens of thousands of these plants.
The problem at hand is not just getting rid of heat however, it's getting rid of heat without cooking the Earth. I still fail to see how generating the heat off planet fails to solve that.
