I just don't see self-driving long term tipping the scale in favor of renting more than it is today.
I think it comes down to this: Robot drivers are a nice feature for owned cars, but I don't think it expands the attractiveness of ownership as much as it expands the attractiveness of sharing.
Robots don't make ownership more attractive to many people who would otherwise not have bought a car. How many people are thinking, "I'd buy a car if they drove themselves, but they don't, so I'm going to get around some other way"? Maybe some people, but I don't think many. Most people who own cars are willing to drive them; they might prefer to read a novel on that desert roadtrip, but having-to-drive isn't a deal-killer. So your new customers are people who are willing, but unable. Is that a lot?
But how many people are thinking "I'd take a robot taxi, but it doesn't exist yet, so I'm going to get around some other way"? More, I think. If you can take the driver out of the comparison, the two cases of car rental and a taxi hire, just sort of blend together into unified case. I think that new thing can serve situations where people currently settle for solutions where they aren't really happy, turning more Nos into Yesses. And I also think those situations where people aren't happy, aren't very extreme; if the shared car scenario where just a little better, it would make a big difference. I know that Uber/Lyft tipped a lot of people who were not taking taxis all the time.