I don't see the current technology making car sharing/ride purchasing more convenient than owning a car anytime soon.
I respectfully (albeit strongly) disagree.
I used to own a car and after my ex totaled it (she was my ex already when she smashed the car and we're still good friends) I didn't bother to replace it.
Instead I bought a share of a car sharing cooperative and for the few times a year, when I need a car their offerings are more than adequate.
Granted, there are a few factors that make this arrangement work very well:
Public transport is so abundant and flexible where I live that it's super rare that I ever need a car.
I have, literally, a dozen cars that I can hire on short notice (peak hours like Saturday, excluded) within a 5 minute walking distance. The models represent the range from a Smart to a Mercedes transporter
The vehicles are always well maintained, clean and if necessary outfitted with winter tires in a timely manner
When I need a car, I couldn't care less what model I'm driving, except maybe: a Smart is not too ideal to transport bulky goods
I don't have to bother with the dirty business of owning a car
It's much cheaper than owning.
If you need a car during peak times some planning is advisable. The worst case was when I needed to take a tram for a couple stations to get to the nearest available vehicle.
So, I think it really depends on how it's organized, availability of vehicles and the quality of public transport. So you don't need a car most of the times to begin with.