Only when the power doesn’t come from PV. If it does, you need (three?) times as much battery capacity: the car’s battery, the immobile battery that the car charges from, and the battery which powers your houses (and some industry and commerce) overnight. If you charge your cars during the day, you can use some of the battery capacity in the electric cars, partially discharging some of them overnight to supply your nighttime needs.

Yeah I see what you mean. Maybe everyone will need to commute nocturnally once we're running everything on solar!