One point to consider is in using a home battery to top up a car battery, the benefit of the one lot of energy is being shared across the cycle life of two batteries. It doubles the cost of the energy by reducing the total cycles on the home battery. There are also conversion losses in the cycle with a discharge charge efficiency possibly as low as 80%.
There may be a benefit of being able to swap out batteries, something some EV manufacturers have considered. Two similar sized home batteries, one at home on charge and filling in household gaps with the other in the car.
Alternately the availability of public charging is another way to possibly trade home feedin for remote charging while at work?
