I think self-driving cars can be combined with public transport to serve a lot of these more arbitrary patterns effectively.
In the future I imagine, every train or bus station would have a small fleet of self-driving cars that people travelling nearby could use on-demand. I think this arrangement has a lot of advantages over using cars point-to-point.
The cars themselves can have a lower maximum speed, and lower range because they don't need to go very far, and lightweight, because they're consequently unlikely to get into high speed crashes. This also means your access road network can take up less space, and be more pedestrianised.
Additionally, because people use these cars for last mile transport, the effective catchment area of a station is much higher allowing them to be more viable even at lower densities, and also allowing less frequent stops to cover an area effectively.
Also, once people are used to using transport-as-a-service interfaces, it's much easier to make them aware of new transport options, and convince them to switch. If someone is opening an app anyway to order a ride to the shops, you can offer them a slightly cheaper journey involving a bus interchange. This in turn allows the networks to be more flexible, as you don't need to worry as much about providing a consistent service pattern for people to learn. So if you notice a lot of people go to the shops on Saturday afternoon, you can add a few buses at that time and people will start using it immediately.