Cities where ride sharing services like Uber was banned (e.g. Vancouver) have been getting along just fine with car sharing services like Car2Go[1], Evo[2], ZipCar[3] and Modo[4] for years. Uber hasn't really brought anything new to the table asides more competition to taxi companies though more convenient app services and VC money to drive prices lower.
Because of the per-minute billing nature of Car2Go (as opposed to Avis which is per-hour billing) as well as the convenience of these cars being within walking distance at any point and can be left anywhere within the service area, it is a direct competitor to one-way travel services like taxis. If I'm choosing to use Car2Go instead of a taxi service to drive my fiancé and I to the ferry on a weekly basis or to drive us home from downtown Vancouver after shopping, or I'm driving myself to the airport, then it's a direct competitor with taxis. Keep in mind that in all these use cases, Car2Go and other car sharing services are significantly cheaper than equivalent taxi rides.
There are enough cars in Vancouver that you'll find one within a few blocks 90% of the time, so the argument of "not bringing a car with a driver" is moot unless you don't know how to drive. There's also no surge pricing. It's always the same flat rate.
Boston Metrocab's app predates Uber by years. It just didn't have VCs subsidizing the cost of rides. Which, in fairness, isn't a business model innovation when it's not a sustainable price.
(Also why Uber went on a sustained binge of offering 5$ rides in Boston; they didn't have anything else to compete with BMC on).
Most cities would have no ride sharing industry to speak of had it not been for Uber de-fanging the taxi industry.