My house uses about 500kWh/month, so a typical electric car parked on my driveway for 95% of the time can run it for several days.
20 million cars in the UK are parked on peoples drives overnight. Vast majority don't need a full charge for the following day and people will be delighted to buy electric during the day for 10c/kWh and sell it overnight for 20c/kWh
If they were all electric with 60kWh of storage and can drop to 30kWh that's 600 GWh of storage. The UK's grid usage overnight is about 20GW from memory, so over 16 hours is in the order of 300-400GWh of overnight storage.
Assuming Germany has similar car and demand characteristics, as long as there's enough power during the day to cope with demand and recharging, there should be plenty of storage for overnight usage.