As with phones...
All that's required is 1) that the battery pack can typically last at least an entire day, 2) that they are typically parked for the night where there's electricity available in the wee hours, and 3) they can be fully recharged while not requiring more than several hours to do so. With these three, it's solved.
Justification: People typically sleep at night. Their cars and phones can be recharged overnight.
For cars (being such high power), they should be included on existing Time Of Day metering, so that the Power Company can shuffle them around as required to balance demand in various areas. That's already an existing technology.
It needn't be 100%. It's "typically" (x2) because the minority exceptions don't add up to much.
The upside of having so much battery capacity on the grid is going to be A very Good Thing. Assuming that the charger can also work the other way. Time to write some better standards for this stuff.