Is there a sweet spot where you still experience significant cost reductions but the inconvenience is small enough that you don't mind it? Well, certainly, for some people! But I think the number of people is going to be a lot smaller than many commentators think.
(The only cases I see where there's no increase in the rides-for-hire business after full automation is if the cost of cars drops to the point where there's very little incentive to try to reduce the costs for most people. Given that cars are quite expensive now, that seems unlikely. I can construct a scenario, but you basically have to believe that, first, the additional cost for driverless sensors+software is very low, second, that driverless software is so safe that you can drastically decrease physical safety features on cars, and third, probably that automation drives significant GDP growth).
It's not that hard. For one thing, you don't need to increase the price much, you just need to increase it a little so that you push cost-over-everything riders out of the queue. There are enough of those that whatever capacity is left should be plenty.
And you are worried those riders who were pushed out of the queue will go back to car ownership, but they are by definition cost-over-everything people, so of course they won't do that. If they could afford to own a car they could afford peak pricing.
* To address the mobile depot use case, I've heard of proposals to have storage areas (possibly trunk, but not necessarily) that are only accessible by the owner, not by renters. Even that may not be perfect though, I do see your point.