Guessing it’ll need a megawatt charger to pull that off on an EV size battery.
Good luck getting a 1MW utility feed.
According to https://www.energy.gov/sites/prod/files/piprod/documents/Ses... the technology seems to exist.
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.
10 charging stations, 6 cars per hour per station, 100 kWh per car. That makes 6 MW peak consumption for the whole "gas" station. A capacitor storing 6 MWh (60 cars served, no incoming electricity) would need to have 120 m³ of storage. Google says that a gas station storage size is between 30 000 and 40 000 gallons (110 000 - 150 000 l) so that seems comparable. Another way to look at it - 200 m³ of storage is a building of 10 x 10 x 2 m, without the need to manipulate flammable liquids.
Not sure about the investment costs (the doc says 5 000 cycles but no cost estimate), how long the peaks are and other aspects of running a gas station. Still, it seems the order of magnitude is about right.
https://electrek.co/2021/12/02/electrify-america-deployed-te...
https://driveteslacanada.ca/semi/tesla-megacharger-installat...
However that brings problems with quality control - a worn battery costs less than the new one. Maybe a model where the customer doesn't own the battery?
Fortunately/unfortunately, so much of that energy in ICE cars is wasted as heat, so the effective gap to make EVs competitive is much smaller.