Here's a potential solution.
At present we drive a big lorry full of petrol from the refinery to the petrol station every so often?
How about we drive a big lorry full of batteries from the power station every so often and take the old batteries back?
Or how about we put a great big power lead into the fuel station. The sort of lead they use for hospitals, data centres, aluminimum factories etc.
You only need to supply replacement batteries to people who are making >500 miles journeys without an overnight stop so the number of people stopping and drawing energy from the fuel station is comparatively low. In the UK you could get away with less than a dozen stations in total on the major motorways (M5,M6,M1,A1M,M62,M25,M4, somewhere in Scotland) and you'd cover almost every non pathological 500mile journey you could do. Really, that's replacing the entire petrol station network in the UK with less than 12 battery stations.
Actually that's probably overkill. Starting from London, Aberdeen and Inverness are the only cities that's far enough away to need a recharge (535miles/560miles). It's entirely possible that the number of people needing a battery swop on the way would be so low it would be uneconomic to make the batteries swoppable or to fund a battery swop station.
Besides, in the UK you're strongly recommended to stop for 30 minutes after every three hours driving. At most that's 210miles of energy every 30 minutes, that's a delivery rate of 180kW to the car while it charges. That's difficult (in particular getting the battery to accept the power without overheating) but may not be impossible.