Motorway services could be an issue, they would need to increase there capacity to accomodate many cars filling up for maybe thirty minutes rather than just five. Also they would have issues with available electrical infrastructure because when they were built EV's were not on the horizon. If as you say some supermarkets have large parking areas that are underused then it could be a case of diverting EV's to charging points installed here.
Looking further ahead there will become a point where maybe personal transport becomes history, just no way to make it efficient unless you can ensure full occupancy. What is more efficient, an electric bus carrying fifty people or twenty five cars each carrying two people?