The third point is definitely wrong. Once you have a fleet of driverless cars, you can optimize their routes to perfection, have almost zero down time, so you would need fewer cars in general. And less liability.
I dont think thats correct. I dont think you could optimize routes, meaningfully more, that would require, some kind of prediction, of upcomming drives. Its not impossible, but not something that will save heaps of money. And there will be downtime, because rides will follow some kind of pattern during the day. When people are at work, there will be way less demand, when people are going to work, there will be way more demand etc. right now thats kind of offset, by Uber not owning the cars, and not paying for idle drivers.
While you are right in principle, I'm not sure if the downtime argument holds: Breaks of the driver are not paid currently. The car lifetime is probably not set by age, but total miles driven.
Self-driving cars might be more expensive, too, in maintenance (more things that can break) and initial cost. So I'm not sure how much they can gain.