Another straightforward problem with this argument is that the AI doesn’t just have the sun in this hypothetical, it also has the rest of the reachable universe. So the proportion of its resources it would need to spend on leaving us the sunlight is actually dramatically lower than you estimate here, by a factor of 10^20 or something.
(I don’t think this is anyone’s crux, but I do think it’s good to avoid straightforward errors in arguments.)
Another straightforward problem with this argument is that the AI doesn’t just have the sun in this hypothetical, it also has the rest of the reachable universe. So the proportion of its resources it would need to spend on leaving us the sunlight is actually dramatically lower than you estimate here, by a factor of 10^20 or something.
(I don’t think this is anyone’s crux, but I do think it’s good to avoid straightforward errors in arguments.)