Just have the same batteries in the charging station to smooth out power usage? Seems a lot cheaper and operationally less complex than a gas station.
So the peak would be the same, but if there were too many customers then sort of like at a busy gas station people would be waiting for a spot rather than waiting for charging to complete.
Fortunately these batteries have "an estimated lifespan of 50,000 cycles". Also, since there aren't super-dangerous elements in them, they should be much easier and cleaner to recycle/renew - especially with the giant recharge-station-scale ones' we're talking about, which could be designed specifically for that.
And yes it's not always possible but it'll be available in enough places.
If a particular station can't get better lines, then as someone else said they could have fewer charging spots. High load per spot still works out well for them, because they can save space.
Especially because the station would want to have multiple cars worth of energy stored, which means the load is divided among more cells and they don't have to work nearly as hard.
Battery-backed charging stations are already common, because it allows use of cheaper grid interconnection, and use of cheaper off-peak or renewable energy.