When I park my car at my workplace and I notice my badge fell out of my pants (or I forgot it), no problem, I can head back to the car and get my badge. If I take a cab I can always phone the cab central and have them ask the driver to look for the item (of course, this requires honest cab drivers and it will cost me a huge amount of money if the cab driver is already on the other end of the city by the time I notice). No way at all to do so with an autonomous car.
Also, a shift to autonomous cars would prevent another very common use case: after work I might want to do something else before driving home, like going to sports training. So now I'd have to carry my gun and ammo (or my sport gear, or ...) all the time around with me instead of leaving the stuff in my car.
Also, my own car still is freedom: public transport, even in Germany, shuts down after 2200 and restarts only at 0500, and if you're outside the city you rarely have time intervals for buses and trains lower than 20min - often it's more like 40min, 60min or even 120min. With a shared car system, I'd have to wait totally unpredictable amounts of time until a shared car is free, and there's nothing I hate more than waiting.
Getting people off individual cars would require absolutely massive investment in public transport. Might work out in cities, but in rural areas there's no way you can get people to abandon their cars.