Adding On-demand bus service to the transit equation
Here’s something that might help improve mass transit ridership in systems struggling to gain traction: Institute an on-demand bus system oriented around existing rail lines. It basically works like this: You have several buses that serve a certain rail station. Buses go out on-demand to someone’s address and pick them up and bring them to the rail station. These buses also serve to take people coming off the train to an address of their choice. This would truly revolutionize public transport by making it truly door to door. In areas where TOD is a long time in coming, it makes rail transit a viable choice for suburban areas without needed these huge park n ride facilities around stations. It can be easily instituted and it’s still efficient since buses can pick up or drop off 50 or so separate people a pop.
There is the issue of a public service taking business away from the private sector, and doing it at what will inevitably be a financial loss doesn't help matters.
But perhaps once autonomous vehicle technology becomes a reality/commonplace, . fully expect transit agencies to work out deals with local taxi companies (there will be many companies running autonomous taxis for-profit) in order to make certain parts of the transit fare discount from the taxi fare, and visa versa. It will amount to pretty much what you are proposing.