Mass transit is a different issue. A good mass transit, which holds to a schedule, does not have the same built-in variability that an "everyone is an Uber driver" scheme has.
My ferry example, for example, is mass transit. If I live in the countryside, and have an hourly bus or even twice daily bus, then that's both a maximum time to wait, and a schedule I can plan on, while Uber for that case will be highly variable and therefore difficult to plan around.
Other issues are only specific to the Uber case. If there are no personal vehicles then there's no need to worry about teen drivers with a sunset driving curfew or people with a restraining order who are nevertheless obligated to pick up a passenger.
I am hard pressed to think of a future where "society might no have a choice", but where your proposal makes any sense.