It seems clear that Uber's long-term plan is to get rid of the drivers entirely. Self-driving cars are in our near future. Having humans drive them for now is a plan to achieve mindshare while they wait.
Getting rid of the drivers means they can't really externalize the cost of the car like they do now, especially fuel and maintenance. I would not be surprised in the least to see their fares go up substantially if this happens.
Who says Uber needs to own the cars? They can rent them from their owners or from car-rental companies.
Imagine taking your car to work and then instead of parking it, letting Uber "rent" it until you go home.