You can build battery towers or underground battery storages depending on the physical constraints maybe? If its feasible, it can also be beneficial from renewable energy standpoint as they also need the storage.
There are obvious benefits for convenient portable consumer devices, though. The benefits seem to outweigh the downsides, and all things considered, there's not much raw materials per-capita.
Electric vehicles are cool and fun to drive, but the benefits seem less obvious. Gas powered cars work very well, and if you look at the entire carbon cycle, it seems like they actually aren't all that bad relative to EVs. A lot of raw nasty materials to build EVs, by many orders of magnitude per-capita.
Going to batteries for wide-scale energy storage, for a vast EV charging network, just seems like a massive waste of resources. I'd rather those precious raw materials be used to build smart phones, sonic toothbrushes, and revolutionary new stuff like delivery drones, for an indefinite amount of time until a better battery technology can be developed.
You could use batteries as the buffer, though. Most batteries support higher discharge rates than charge rates, which is nice for longevity. You would need a battery pack the same capacity as the car's in order for it to really make sense. You would also probably use lower density cells too, since they don't need to move. They wouldn't fit into the user terminal, so you'd probably locate them in a nearby shack, and run very thick cables. If you had more than one charger, you would probably have an even larger shack. Before you get to millions of battery cells to manage, you might step back and realize that something like a giant flywheel would make more sense, and then you're only one or two steps away from building a power plant.