for example around 6pm EST the sun goes down on the east coast, however in on the west coast there's another 2 hours of daylight- in the early evening the surplus power from the west coast would handle the demand spike as people on the east coast come in for the evening and start turning on the lights. The reverse would be true in the morning, the east coast could preload the system for a couple of hours as peoples coffee makers and office computers fire up in the morning on the west coast.
Storing the energy instead of burning it off over long haul cable runs could also potentially make the grid more efficient, with the batteries acting as capacitors and smoothing demand spikes and voltage transients - making it somewhat more reliable as well.
Its really not a bad idea, but is gonna require a lot of manufacturing, testing, and getting agreements in different states with different laws and regulations.
the engineering and work are gonna be rough, but i'd guess the paperwork is where the bulk of your time winds up going.