Balancing systems do exist - I used to swim in Smith Mountain Lake[1] as a kid and that entire lake is a gigantic battery. During low demand periods they pump water into a reservoir to then run the turbines during peak demand hours. None of these systems are perfectly efficient - but we've got a lot of options in our tool belts for ways to balance peak demand that don't require more continuous production capacity.
Yes, pumped storage does exist, but to provide a nation sized battery using pumped storage, you would need to use two of the Great Lakes and pump one of them up by 200 feet.
The power needs of the occasional cold wind still winter week are fairly large.
