So in theory can normal cars. Many taxi companies (and I'm assuming at least some Uber drivers) share one car between 2-5 drivers to maximize the time on the road.
The other aspect you're not considering is that even after you take economies of scale into account a driverless car will almost certainly cost more than the market price of the current median Uber car. I'm guessing that $3000-5000 will get you a perfectly Uber-worthy car that will give you years of fairly trouble free use. What will a driverless car cost?
And that is ignoring the fact that most Uber drivers would have owned and maintained a car even if they had had a different job, so the only 'cost' is the marginal cost of extra maintenance being used as an Uber car causes.
Also I wouldn't be surprised if maintenance costs will also be higher at least in the short-to-medium term due the complicated and experimental nature of the components involved.
So even if there are long term savings I imagine that they will take a long time to materialize and even longer to show up in fare-prices, unless Uber decides to subsidize driverless fare to kick start the market.
And if they are not first with driverless cars, big national cab-companies are also in the run.
First, efficiency of utilisation: Driverless cars can be driven around the clock (modulo maintenance and refueling time), so car depreciation/maintenance gets amortised amongst more passengers.
Second, efficiency of scale in maintenance: It is extremely unlikely that the maintenance costs that uber drivers take on - buying parts retail and taking their car to the nearest garage for repairs - are lower than what would be a dedicated factory-like maintenance shop for thousands of automatic cabs.
And third of course: direct wage costs of the driver once you subtract car maintenance from fares is still a lot bigger than zero, so eliminating that saves money.