If its infeasibly expensive then so is Nuclear. For the same money as a nuke you can install 60GW of solar - near twice the counties needs. It would generate more than the nuke would in their respective lifetimes, Once you have that kind of spare peak load going for effectively free then someone is going to work out how to store it one way or another so its available all the time.
As for fast charging cars its always worth remembering the London Tram Company could change a battery in a couple of minutes in 1910 or something. No reason why cars cant be designed to quickly swap out batteries - apart from people who think that people actually think their car says anything about them.