For cars, the factor of three is not "optimistic", it's simple comparison of the respective primary energies consumed by typical vehicles in their respective categories. 20 kWh to drive 100 km = 72 MJ of primary energy. 6 liters of gasoline to drive the same distance = ~220 MJ of primary energy -- roughly triple of the former number.
> A week doesn't sound totally crazy to me; we certainly want a good safety margin so that society doesn't collapse in a bad winter.
Yes, but that doesn't imply you need the capacity to run the country 100% on batteries for a week. That's just not something anyone would ever do. For example, a gas turbine with a low duty cycle would definitely be cheaper than a battery after a certain period of time. So why would you use a battery for that?