The end goal is for public transit to reach the convenience of the private car (or to substitute that in another way). In many European cities this is already the case for personal transport. For instance in London it's usually faster to take public transport than drive, especially so in rush hours. The public transport infrastructure can cope with this demand. The road infrastructure, on the other hand, can't really cope with the number of people who want to drive -- roads grind to a relative halt. The average speed on London roads is about 10 mph during day time and even lower during rush hour. Some dream of car ownership, that. Thing is, this kind of pattern is seen all over the world in big cities. The only way to escape it is to not live in a big city, but about 70% of the western world does, so you can't ignore it.
I think that as autonomous vehicles come about the model of private car ownership will get completely shaken up. People will still own cars, in some cases it will be more convenient. But if you could get a car on demand at a similar convenience to owning a car, whilst having none of the inconvenience and fixed costs that owning a car entails, that could be pretty attractive. The real benefit here is optimisation. You often don't need a 5 seater car, not for your commute and not to go to the shop. You'd be happy with a 1 or 2 seater. So that's what you hire. If you're going to the airport you get the 4 seater with extra luggage space. (But that car doesn't park at the airport - it drops you off and then gets another customer.) If you're going to buy a sofa you hire the auto-van with space for your load. No more buying a massive SUV because twice a year you go to the dump and you'd rather not do a second trip. On the highway all vehicles heading in the same direction join together in a convoy to maximise range and efficiency. It changes the dynamic of a private car completely. It also dispels issues with range anxiety, because for a long trip, you just hire the 150kWh car, but the small car is using a 30kWh battery.
Autonomous vehicles is where public transport is heading. Of course autonomous technology needs to catch up, it's still in the nascent stage, but it's coming. It's really going to endanger millions of jobs too, but that's another discussion.