The op's point which you failed to comprehend is the less often you cycle a battery the longer it lasts. So the overnight cost per joule delivered is constant.

The op's point which you failed to comprehend is the less often you cycle a battery the longer it lasts. So the overnight cost per joule delivered is constant. You could object to the amount needed up front, or use some reasoning based on discount rate, but you didn't. Also it would be wrong even if you did because the energy needed for the infrequent long duration events is a small fraction of the total and doesn't need storing inna chemical battery. Even using gas for it for centuries would release less emissions than the emissions released whilst building the nuke instead of something reasonable.