I don't think those numbers are optimistic, I suspect they've already designed the sat in CAD and that's what the calculation spat out; it's probably quite accurate. The physics of this sort of thing are quite well known and SpaceX already has experience with the type of satellite that will be needed. There's no need for them to rely on napkin math.
Cost is a different matter of course, but it seems incongruous to me that after being confronted with the fact that your power density assumptions were off by a factor of 2x you would continue to insist ChatGPT's weird assumptions about manufacturing costs scaling linearly with mass are accurate. As was already pointed out upthread, even if all the calculator's other assumptions are correct they can turn a profit if they get the per satellite cost (excluding the cost of the GPUs) below $2 million. I think the only big question mark here is launch cost.