Have they even talked about how they’re going to handle the heat?

I’m willing to believe the construction is plausible (maybe not cost-effective, but possible), and robotic operation of it is a stretch but with some optimism I could be convinced.

I don’t see how they can get rid of the heat, at least in a realistic way that isn’t “a square kilometer of black body radiation surfaces” or something equally “works on paper, so uneconomical it will never actually happen”.