[SuperStar3000]

Uber/Lyft/Google/other are waiting for self-driving cars they can "make a killing off of." Wait until they have to do maintenance on vehicles they own...

It won't cost them anything, because they will not actually "own" any cars.
All costs, risks, and liability will be shifted to third-party fleet operators.

 

[SuperStar3000]

So, third party operators will be working for free?
Who will be funding them? I'm curious to know.

Who do you think is currently funding the Uber cars? Third-party operators (aka Drivers).
When autonomous vehicles become prevalent, a driver contractor who is currently operating a single vehicle will be able to own, operate and maintain several autonomous vehicles.
Just as it is now, operators will be paid for the use of the cars, but Uber will not be responsible for any of the costs or liabilities when something goes wrong.