>By which I mean, what problem or need are they addressing, that couldn't be better served by improved public transport?
Driverless cars will eventually converge with public transport.
-The only public transport that travels from door-to-door at the time the user wants is a taxi - and that is expensive for the user because the human taxi driver needs to make a living.
-Human taxi drivers are known to work until they have made a certain amount of money each evening - on rainy nights they make this amount of money more quickly due to higher demand, then go home - this is why it is hard to find a taxi on a rainy night. (this is explained in the book Freakanomics)
-Driverless cars would allow for traffic junctions that don't require vehicles to stop and start, thus improving fuel efficiency and engine life.
-Driverless cars be instructed well in advance to move to the side of the road, meaning that emergency vehicles can travel faster.
-Driverless cars can improve the capacity, fuel efficiency and safety of motorways, by travelling in networked 'trains'.