Living in a city that has decent but not great public transportation (God I miss the ESWE buses when I lived in Weisbaden), and having 2 kids, I don't ever see this happening. The wife and I both work with Jobs over 20 miles apart. The kids have soccer and softball, at fields sometimes as far away as 25 miles away from our house. There is just no way that a rideshare would ever work, or be easier than owning cars to be able to independently go to where we want or need to go.
Also, what happens if in the evening or middle of the night you have a non-emergency emergency and need to go to urgent care or the emergency room? Paramedics cost about $1600 per ride around here and not to mention the paramedics are already extremely overworked as is.
My use of the word ride-sharing probably wasn't correct, as what I meant was Uber in general, including taxi-like Uber and UberPOOL. The thing is, once self-driving electric cars become widely available, the cost Uber and similar services is going to plummet. Right now the biggest costs are the driver and gas, so once you eliminate those two the cost will be minimal as you only have to pay for electricity and deprecation of the car (Uber or similar company of course takes its profit too). When the cost of Ubering becomes nominal, why would one spend tens of thousands of dollars on their own car and take the burden of storage and maintenance on their shoulders as well? Owning a car just doesn't make financial sense anymore. Of course, rural areas are an exception as it doesn't make sense to have an Uber car nearby, making the waiting time too long.
With the cost being low, the distance becomes a non-issue too. I don't see how low-cost self-driving electric Uber wouldn't work in all scenarios you listed. Just take an Uber from home to work and back. Have coworkers living on the way? Ride-share with them to save even more. Same goes for kids - if they are old enough they can even drive alone, so no more driving to every practice and game multiple times a week. In case of a non-emergency emergency you may already need a cab if you had a few beers during the evening, so a cheap self-driving Uber just makes it better. Remember, self-driving cars can drive around 24/7 (well, they need to be charged but not all at the same time like humans who tend to like to sleep at night), so getting one at the middle of the night won't be an issue either.
I'm not saying this will happen soon because it will take decades. Most of the currently driving population is used to owning cars (like you) and it's going to be difficult to change the attitude and habits of those people. They'll likely adopt self-driving cars at some point, but most will still insist on owning their own car because of old habit. It's the younger generation (i.e. people who have never owned a car) that will adopt the shared-car economy and it will spread and become a norm from there, but it will take looooong time.
Obviously, there's going to be regional differences as well. I suspect the US won't be at the forefront of this (excluding the SF area) because owning a car is like a civil right over there and I don't judge since the public transportation is pretty much non-existent over there in most places. For me as a European and as someone who used public transportation all the time during underage years, it's going to be a smoother transition. The ridiculously high car tax helps too I guess.
Regulation will also play a big role as it can either boost or slow the adoption down. First of all, human driving needs to be banned because the requirement for efficient self-driving cars is that all cars are self-driving. Human-driven cars are unpredictable and cannot communicate with other cars in the same way that self-driving cars can, which is what makes self-driving cars so efficient (everyone driving at the same speed, perfect exits/enters, etc). Unfortunately, we all know that governments can't just ban human driving and normal cars overnight, so it's going to be a long process.
