The pace you can shove power into batteries drops as they get fuller.
What some places seem to be planning is installing some large static batteries plugged in to help average out the power draw from the grid whilst allowing fast car charging. So instead of giant 250-350kW spikes they draw a much more sane 100kW from the grid, when the slots are empty they charge the battery, when the cars charging fast then it draws from the grid and the battery and when it's slow it charges the car and the battery.
There is talk about building in PV into charging stations, which makes sense if you can do it. They already have the grid connections.