It would probably be easier to have charging stations with people hot-swapping batteries, than charging station with extremely fast charge times. It would be a task that could be automated right out of the gate too.
I like this idea too. Because battery positioning within a car is quite important (at least what have read about the teslas it is) there could be a smaller 100km (60 mi) range swappable battery that is easy to remove and replace.
It might even be feasible to have a system like a drive-through carwash, that instead lifts specially compatible EV's, remove the old battery "strip" from the lower portion of the car, and then install a new one. If it could get down to 3-5 minutes, especially if your car could interface with the "hut" so you don't need to be in it...
Elon Musk demoed Tesla's battery swapping capability a few years back: https://youtu.be/FE81S26XG8c. I'm not sure if it's gone live at any supercharging stations yet. Maybe someone else can confirm rollout or not.
See that is just incredibly cool. I honestly see no reason why they, or someone, shouldn't be able to make it work. The barriers would probably be having enough of an installed userbase, but that's always the problem.
No-one wants to own a depreciating asset like a battery. The model would be something like "pay $x/year and any member of our nationwide network will swap out your battery for a battery with at least 100 miles' worth of charge, whenever you want". They can take care of replacing worn-out batteries on their side.