Perhaps.

If a station has a lengthy peak period of use, then perhaps the batteries would need to be huge.

The number of discharge cycles required for the batteries also matters, as does the conversion losses (charge, discharge). Replacing batteries after end-of-life could be a significant expense. I am guessing the savings from off-peak charging cover that expense given that some charging stations have storage batteries, but at a guess the cost implies ≈10% systemic ecological cost on top of the power charged to the vehicle.