My car has 100kWh energy storage and spends most of the day plugged in. Discharging 20 kWh around the optimal storage point will not hurt the battery. If we reach 20 000 000 cars like that we have 400 000 000 kWh or 400 GWh at our disposable most of the time .

Cars alone could handle about an hour of the national grid, assuming that Energie intensive industries would not shut down temporary whenever the price of electricity is high/ predicted to be high.