So why not smooth it out? Put another battery in the charger which slowly replenishes. Then the grid doesn't see the bursty load you're talking about.
There are 1.4B vehicles one earth, the plan apparently is to replace them all with battery powered vehicles
I don't think people understand the scale of this and how many batteries we can produce and recycle given the limited resources we have.
Most of which spend approximately 90% of their time stationary and unoccupied.
You can't have batteries to charge batteries, then you'd need batteries to charge the batteries charging the batteries. All of that because we simultaneously decided that nuclear was bad and all we need is windmills, which are like the worst thing to power a fully electric world with high demand peaks, and to move from gas to electric cars
Adding batteries won't solve any problem. Gas allowed us to live unsustainably and made it easy to do so. Wanting to replicate that with electricity/batteries is plain stupid.
If everyone needs three tonnes of steel and their own body weight in rare earth material to cover 30km per day on average we're totally fucked from the get go
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.