A majority of the use cases for self-driving cars are either solvable, or already solved, by some combination of better urban planning (i.e. zoning and probably large-scale regulatory reform), public transit (specifically useful public transit), and public investment. Unfortunately, in the United States, we are unable to do even one of these things sufficiently well, hence the need for self-driving cars (or, in some cases, some other technological solution; e.g. hyperloop).

I don’t know, can a train take you from any arbitrary point to any other arbitrary point?

Yes, from the train station inside my garage to the train station inside the hotel. /s