What people fail to take into account is the self-driving car future where Uber takes 100% of the profits (since there is no driver). It will start taking a chunk of the people driving themselves market as well when Uber becomes more convenient and cheaper (removing the human allows them to be more competitive with every day driving).

To get to this point however does require it to start operating its own fleet (unless small regional companies form to manage the fleet and just loan out their self driving cars to uber). Either way Uber is in a good position. If it manages its own fleet, it can better negotiate the price of each car than any individual can. It will also have more data than anyone else on how those vehicles operate and can then buy it's own insurance for its entire fleet, cutting costs there. If the alternative occurs, then Uber will own the buy side of the market and have most of the leverage relative to local companies that manage their own fleet.

There are a lot of ways things can pan out, but being the most tech focused of these companies with the best engineers of any of these types of companies, puts it in the best position to own the self-driving car future. The only company better positioned is probably google.