That's why electrification of transport will be good for the grid.
Cars can charge at night, or any other time when energy supply is abundant and/or demand is low, and export back into the grid at peak times with V2G. Storage batteries on wheels!
People charge their electric cars overnight. Water in the hot water tank will stay hot for a couple days, so it makes sense to heat that at night, too.
In hot weather, you can also run the energy-hungry A/C at night to cool a tank of water or a block of masonry, then use that during the day to cool the house.
The reason nobody bothers doing that is because the price of electricity is the same day and night.
Why would it be inefficient to charge your car battery at night? And storing coolness in a masonry slab doesn't sound inefficient to me. Pumping water uphill and running it back through a turbine is pretty inefficient.
I was referring to the cooling part, not the car charging. My totally unsubstantiated gut feeling is that a piece of concrete or a tank of water wouldn't stay cold long enough to be useful. With my local company, electricity during the day is something like 20%-100% more expensive (less of a differential in winter, more in the summer)