But we generally don't need to satisfy the peak with battery - peak US demand occurs while the sun is still up, in July, so you can satisfy a large chunk of that with solar still. The hard part is those ~4 hours after solar stops producing enough and it's still hot and people are still up. So what we need is several hours of about half the gap between {nuclear, wind, hydro} and peak. Remembering that we also use even non-pumped hydro as a form of storage, by drawing on it more in the periods just before and just after sunrise/sunset.

For example, if you look at the energy production across PJM from two days ago: https://cdn.bsky.app/img/feed_fullsize/plain/did:plc:hiovtnl...

(Using that b/c I run the bot and it's data I'm very familiar with. You can see similar patterns in CAISO but they've already got so much solar it's a little more messy/duck-curved by all of the behind-the-meter solar.)

You can see hydro coming online from roughly 16:00 - 23:00. There's still a big gas peak that we'd need a lot of storage to shave, and you're right that it's a long way to go before we do that, but it's not quite as bad as "we need enough battery to satisfy 100% peak demand".

As others have stated, neither storage nor generation is evenly spread.

But, like with UPS, 96 seconds is ample time to let delicate systems glide to a standstill or to start the diesel generator.