I can’t tell if you’re joking? Today the drivers buy the cars. A driverless car can’t buy itself, so some entity will have to, and if it is not Uber itself buying the car whoever did buy it will want to get paid just like today’s drivers do.

I'm not joking, and you seem to have missed the entire reason people think of self driving cars + ride-sharing services as being a game changer.

Today people drive others around for money. Tomorrow people let their cars drive people around for money. No one thinks Lyft and Uber are going to be buying the cars, people just won't need to be physically in them to make money from Uber and Lyft any more.

Just because self driving cars are a game changer doesn't mean that all (or even any) of the benefit accrues to Uber. Who holds pricing power in this scenario? The company that makes the car, the person who owns the car, the agent (Uber/Lyft/etc.), or the rider? I think there's a reasonable case to be made that the agents are the most commodity-like element. Tesla e.g. has already shown a desire to use value-based pricing to capture their share of the money-making potential of the cars they sell. Any owner will prefer to rent their car via the agent that pays them the most. Any rider will prefer to rent it through the agent that charges the least.

While I disagree, that's at least a valid argument. You should start with that instead of asserting that the capital requirements of buying up a bunch of cars will be the limiting factor.