I wonder how the fossil fuel distribution deals with the same problem. Stations have big underground tanks, so if it is true that they only see high demand twice a month, you'd imagine that the tanks and the actual dispensers would be over provisioned for most of the month, and that peak usage itself might lead to queuing (but no shortages, it sounds like).
Now obviously batteries are much more expensive than fossil fuel tanks, for any given energy capacity. But eventually I would think it could get there.