The UX is such a minuscule part of the business compared to the logistical operations that Uber/Lyft don't have. (Remember, Apple always had the UX. What made it rich is the supply chain, which is why Tim Cook is CEO.)
I'm not sure why the downvotes, you're basically correct. I really don't care much whether it's a person or a computer driving me around. What I care about is the price.
People seem to implicitly assume that autonomous driving will make getting driven around really cheap. But all you're really doing is taking a ~minimum wage driver out of the loop. A good starting point for costs is the $0.50ish/mile IRS mileage deduction which is maybe about half Lyft/Uber pricing today. That's a significant difference but I'm not sure it's a radically alter everyone's behavior difference.
The only theoretical differentiator is price. At the moment VC subsides are removing that as well