Non-governmental subsidized transportation infrastructure is and always has been a race to the bottom. Taxis are mostly only profitable with extremely low overhead and only servicing high traffic areas like Manhattan or other major metropolitan areas.
Uber's thousands of engineers and SF HQ disqualifies them from being low overhead anything.
In the 1890s in Chicago when massive subway and interurban train networks were built out by private business, they either failed financially or succeeded only by real estate speculation around where they built their lines. Eventually all of those lines were acquired by local governments or shut down. Mass transit lines in LA, NYC and around the country followed similar trajectories. Look up the Interborough Rapid Transit Company in NY, or Charles Yerkes and Sam Insull in Chicago.
These days modern suburban subdivision companies don't bother with creating mass transit, they just fund street construction and install public works lines like gas/sewer/water/electric, and let the city deal with the traffic and the inevitable deferred maintenance that clashes with their low tax philosophies.