I fail to understand why you think that private ownership will fall just because of AVs.
I don’t share my slippers with my next door neighbor when I’m at work, nor my wife or my bed, why do you think I would want to share my transport ?
The only reason people share a bus/train is because there is nowhere to park when you get to work, my AV can drop me off and then fuck off into the wilds and do its own thing till I want to go home and my choccy biscuits will still be on the passenger seat where I left them.
AVs will produce a boom in ownership as all those people who can’t, hate or are temporarily incapable of driving will breath a collective sigh of relief and abandon public transport forever (including taxis), I mean, have you ever been on a bus ?
Ubers business model is junk (they are just a glorified taxi controller), taxi usage will fall when AVs are adopted, they might be able to do holiday rentals but that is about it.