Seems like a very complicated business to get into compared to chauffeurs, no? In Paris, Uber doesn't seem to handle cars at all. The drivers buy/rent cars from wherever and drive. And drivers are in charge of their car's maintenance, repairs, etc. Uber provides the smartphone apps and underlying platform. That's a challenge in and of itself, but not at the same challenge as maintaining thousands of vehicles I would bet.

Although car rental is well overdue for some disruption, I don't really see how Uber overlaps with it. I typically rent a car if I need to go long distances for multiple days, typically to remote areas where Uber doesn't serve (I currently write this from the Piedmonte mountain region of Italy).