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With batteries that would have a multi-day cycle like these ones, you're going to be trying to flatten out the demand curve (and supply, but the two are related).
The US generates 4.2 PWh a year, and so averages a consumption rate of about 480GW. So, in an ideal system we'd only need this level of generation capacity and if it was higher sometimes and lower others the batteries would smooth it all out.
I'm going to take your 560GW figure as representative of normal demand above the 480GW average. I'll say half of every day is 80GW above average (when we'd be draining batteries) and half is 80GW below (when we'd be charging). The real curves are much more nuanced, but we're establishing context. 80GW for 12 hours is 960GWh, so let's call it 1TWh of battery capacity needed for the whole USA to smooth out a day.
That's 117 of these installation, which frankly I find amazing that it's so low.