It should be cheaper. And it will feel less like you are beholden to another person, I think, and more like it’s “your thing.”
An autonomous taxi can just sit in the parking lot at a job site until it’s called again, too, if parking is cheap. No need for it to “go home”.
Other benefits of a taxi over driving yourself are that you can be drunk, you can take a nap, you can read a book, … while you are getting from here to there. And no one will feel rude ignoring the car’s autopilot.
I don’t think they will eliminate private ownership of cars or anything, but I think they will reduce private ownership of cars, and open up a lot of places to be car-free that are currently car-required.