What if you kept all your car stuff in some sort of modular compartments that could be easily loaded and unloaded? At the moment there isn't much incentive to do so, but that might change with this scenario.
What I'm getting at is while your argument seems sound, and may in fact prevail, when you change one piece of the puzzle sometimes other solutions become possible.
Maybe your driveway is replaced by a compartment container. Maybe (certain kinds of) cars will be able to automatically load the compartments. Or maybe you're completely right.
I can't leave my stuff in the street, especially since it isn't the same location every time I park. In other words, there's not necessarily a dedicated space that will be empty if I'm renting instead of owning, let alone one that I control
In fact, folks who don't have dedicated/owned spaces are probably the best audience for rentals.
Moreover, even if I'm willing to take said stuff into my residence, I may need said stuff on my way to the drop-off.
It's getting kinda pointless. I'm suggesting something that might happen in a future where self-driving cars have completely disrupted all of transportation. You're countering "there's no dedicated space" - well, just maybe, that can change? It's not even a full space, it's just a "dock" to load the containers.
In fact, even today, people who don't have a dedicated space (even if that space shifts around a bit, ie. is a "pool" space on the street) can't own a car: Where would they leave it? People who are renters today already have to deal with not leaving stuff in the car, so this discussion doesn't apply to them.
Long story short: Your original argument was that not owning your own car will not be be an option for you, because you leave a lot of stuff for your kids in your car. My argument is that, with a bit of fantasy, maybe this isn't an insurmountable obstacle.
> I may need said stuff on my way to the drop-off.
Why would you drive your self-driving vehicle to the drop-off?
One of the small but nagging issues which will need to be resolved is how to deal with "items left behind".
When more people begin to use public cars for personal use/hire people will begin leaving phones, strollers, jackets, wallets in these vehicles. Unless the cars are to have omnidirectional cameras or electronic trackers to monitor everything, people are going to lose things. This is going to be a pain point. It might be just becoming aware -as people do in taxicabs but at least honest cabbies will return items as its in their interest to maintain good reputation --a stranger is only bound by altruism.
What I'm getting at is while your argument seems sound, and may in fact prevail, when you change one piece of the puzzle sometimes other solutions become possible.