I don't think this will hurt Uber at all. This has been their plan all along.
The biggest PITA for Uber all these years has been paying those "pesky" drivers. That's why the've fought so hard to not have to treat them like employees. Or human beings, for that matter.
I think as soon as Uber can buy a fleet of self-driving cars, they are going to make more money than ever. And everyone driving for Uber will have to find work elsewhere.