For the record, I drive a stock car. I like few extra comfort bits I got, but many cars got that these days. I'm fine with people having fun in a way I don't get though.
The point about storage and kids is definitely interesting. Seems like potential for business opportunities if we ever find ourselves in this world.
I guess bottom line would end up ~ the same as current car sharing services. Cheaper if you want occasional use, but more expensive as daily driver. And availability issues at peak times.
Current car sharing service (e.g. zipcar) is virtually the same as autonomous car sharing. You're not removing any large costs. Fleet balance is arguably the only cost removed. But it seems to be more or less solved problem even without autonomous cars. At least in my city, they no longer require to return (most) cars to the same lot. Wether car is autonomous or not, you still have to purchase the vehicle, pay insurance, gas, maintenance... Same price. The only change would be paying for idle car, it could drive back by itself. But user would have to pay for those junk miles. Which may be the same as paying for idling in the long run.
If car sharing service would want to have good availability at any time, they'd have a lot of overhead cars. Which would increase the cost. Otherwise they'd have to have reservations. And we get into a whole can of worms..
The random self-driving car is pretty much the same as public transport. Individual cars seem to be still a thing, even though we have buses, taxis etc. Having random car pick you up is not some totally new idea that wasn't tried ever before.