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Outside the cities and commuter routes to/from them most train services are crap though. One train an hour (which may or may not turn up depending on whether the train company has bothered to get enough drivers for the day) which proceeds to stop at every tiny station between you and your destination. People will need no encouragement to move away from them.
I see express train routes between the cities and then self-driving cars picking up at the station and radiating outwards.
This isn't going to change until all drivers are off the road and motorways move on to supporting convoys of cars at 150mph+ which I can't see happening in the near future.
I doubt this very much. 'Self'-driving precisely levels out one key advantage of rail travel today, that people can work while they're on the train. While ownership of cars will probably move away from the individual, it's a fairly well-publicised fact that the car companies see the future of their business models in building cars, not selling those, and instead charging for trip hire. The aim is to undercut public transport and to effectively privatise it. This would obviously not be possible in the inner cities, but outside them it is a distinct possibility. Obviously, it's all speculation at this time, but I think this is a much more likely direction for it to go in.