Except that you also have to move the electricity into the car, which is actually the limiting factor in Teslas today, not the batteries. So this wouldn't really help at all.
Tesla is attempting to solve this by building a massive battery storage capacity into the chargers and then trickle charging these batteries when the charging bays are not in use, so this is by no means a problem that has been solved once and for all.
So you are correct your average distribution feeder probably does not have capacity for a 10 mw service. I guess that's not much of a shock.