Some sort of scheme like they have with those bloody scooters could be a solution.
Electric cars, unlock with your phone, pay as you go. It would be great if they were driverless cars It won't replace private ownership but could reduce the number of cars on the road. If it's cost effective, people who just need a car to go to the shops or pop round to see friends and family could go for it. Use the train to get between cities and pay as you go cars when you're there.
The scheme probably exists somewhere, I think it sounds reasonable on paper, but not sure what it would be like in the real world