But then we need to wait for the charging station to charge. How many of those batteries would a charging station need to ensure continuous service?
E.g. Honda is working on it: http://www.honda-mpp.com/in/
And people are already attaching batteries to the grid to earn money by smootging supply and demand, it just makes sense to locate those near to demand so they can share cables. Then to the grid the car charger station looks like a consistent energy user that can flex a little to help the grid (possibly even feeding back during peaks), rather than a random one.