My current thinking goes into the direction of small private electrical golf carts for cities since those fulfill the most important requirements given to me by those who say they'd never want to give up their car. One could even make them foldable and stack them upright when parked. Slow speeds mean that not much of a safety buffer is needed in the material.
Being able to make longer trips in the same vehicle is surprisingly low on the list. It is given mainly by people with kids who want to load the vehicle in front of their house and not have to pay for several vehicles (thus having a golf cart and a normal car does not sound appealing).
Maybe someday. The problem is that there isn't really a sharp divide between dense urban core and everything else. I think about the largest city nearest to me and traffic can get pretty high speed even nearby fairly dense areas. Traffic is often jammed up but when it isn't it doesn't just move at sedate speeds.
Many golfers carry their clubs. The chess guy has his chess set in the car. Shopping bags from the lunch break shopping trip - all things you live in your personal car. Sure you can carry them in, but you don't want to.
Parking is one reason given. Maybe. But if you don't live and/or work in a dense part of a city, parking isn't a big issue. Feel free to argue that people might be better off if there were less parking but today's reality is that a lot of people don't have any parking issues on a day to day basis.
The bigger argument is around improved utilization. But the cost of owning a car is usually more about mileage than time and shared vehicles will actually have to travel more miles because they won't always be transporting a passenger. There are some age-related costs, especially in states where it snows. Yes, some people want the latest and greatest but then they have the option of leasing today.