If we’re talking about short term, like within the next 20 years, I think what you’re describing only applies to dense cities. Places that are more spacious, with lighter traffic and not much public transit (like my home area), will still be dominated by personal cars because it’s simply more convenient than trying to coordinate your plans with things like Uber. Just as we (here) only have taxis for trips to the airport and an occasional trip home after too many drinks, so too shall Uber and Lyft only work for those really committed to that lifestyle, or for the same seldom necessary use cases we use taxis for. Now, if personal cars become as cool as our smart phones, I would guess that people here would only be MORE excited about owning a car, not less.
Indeed, this personal freedom to travel on demand is one of the things people like about being here. My sister and I each separately tried living in Chicago and gave up on it. For both of us, the crowds and the lack of ease in getting around quickly and flexibly was a real turn-off.
And while I’d like to agree with the commenter who implied that telecommuting (and similar) will reduce the need to travel anywhere, this vision is a bit in the distance. Firstly, there are many jobs that cannot be done remotely. For those that can, there is still a big cultural problem in that most companies don’t trust remote employees to do their work, or simply don’t think the right atmosphere for teamwork can be fostered among a collection of remote employees. As someone who suffers severely from S.A.D., I long for the day that I can work 100% remotely, at least for 2–4 months of winter. I think I’d be a great deal more valuable of an employee if I could do my job in the warmer and brighter solace of, say, south Florida, for those months. It doesn’t look likely to happen soon.
Again, I’m talking short term. I have no idea what things might be like in 100 years. We’ll be past the singularity by then! ;)