The problem is that there's no significant economies of scale to the taxi industry. You don't make drivers much more efficient by having more of them, and there's an induced demand problem where the limitations of cities and traffic mean that you just cannot scale up to infinity.
This is by the way why there's no enormous single individual taxi company in the existing market. Taxi business tends to be small and competitive for this very reason. It's an extremely ill suited environment for a technology startup.
If self-driving tech really becomes so good that it will make tons of money, then why let Uber etc have that market? There is zero that differentiates them. Everyone can put a booking app together and optimise it over a few years (see the many international copy cats who have done just that).
Then why wouldn't a self-driving-manufacturing leader (whoever that will be, Tesla, GM, BNW, a Geely or other Chinese player, doesn't matter) run fleets themselves? It's not like there's much human cost involved. (and manufacturers already got their service networks and charging networks together where self driving vehicles could go at night to be charged/serviced)