Earlier quoted context omitted.
I was definitely using simplifying assumptions to get my point straight here. Setting the actual parameters for such systems is an engineering job, I just wanted to illustrate that the goal isn't going to have the charging station off the grid during peak hours thanks to the batteries, and more about managing the burden you put on the grid.
Yeah that's why it probably needs to be more than 1 charge in the battery. Unless you do N back-to-back charges during peak time, the charger isn't utilized enough. And to do N back to back charges you need about N car batteries as buffer.
But it's not a realistic assumption, at the very least the driver has to park, get out of their car, plug the car, spend some time on the payment interface, then unplug the car and leave.
So even in the maximum theoretical scenario where drivers are lining up at the charging station, your charger isn't going above 80% utilization. Using a single car battery, you can save 20% in terms of connection to the grid (you “just” need a 800kW connection instead of a 1MW one), and you aren't nearly as much of a nuisance to the grid as if you were having constant ups and down of 1MW.
In practice there will a be a trade off between how much you save in connection infrastructure to the grid and how much you spend on batteries, and this calculation will depends a lot on the usage pattern.