[Hatman]

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.