However, I tend to think that there still may be a decent size of population who'd prefer owning. Others mentioned the convenience of using cars for storage, being readily available, lower cost of owning, reduced insurances, customizations, etc. Along with these, I believe some other factors exist.
In context of self-driving cars, we typically tend to picture urban transportation first. However, there will still be needs for long distance commuting, or taking long trips for pleasure. There will always be places where people frequent less compared to major spots/suburbs in a city.
People may not always want to hop into a random car every time they take a trip. The cost/time involved in flagging a car of your choice may not be worth the effort for some. Also, keep in mind that many think of cars as a statement, another way of expressing their beliefs. Take for example, preferring German vs. American vs. Japanese, some prefer minimal space, others may like to exhibit opulence.
All in all, there will be a large shift towards not-owning cars, but there may always be a market for owning (at least for a long while).
There may indeed be locations where 20+ minutes is a realistic answer, but I suspect those places are more rare than you think.
But I don't think you can get to "every car is self-driving" without a pretty high proportion of self-ownership in rural or exurban areas. Lots of people live ~20 minutes from the nearest downtown-ish area, and you can't really serve all those people without a pretty serious wait.
Minivans are being used in these trials because they can carry multiple people to different destinations. That's the only reason. Minivans suck.
Imagine a boat owner. They need an F-150 with a trailer hitch, plus the wiring for the boat trailer's lights. So if they want to move their boat around, they need to wait 20 mins for something they can currently do right now without waiting, without dealing with network outages, with the ability to tow something heavy.
Look at the sustained performance of a Tesla S at Nurbergring. Towing takes a lot of torque, and will kill a battery like a Tesla. Plus the car needs to be able to get a bit wet/muddy sometimes.
> using cars for storage
While it's true that you won't be able to just stash all your stuff in a car you don't own forever, I think it's entirely feasible to have a system that lets you rent a car for a day to use in this manner. Obviously not quite as good as owning a car, but you can get a lot of the same benefits in limited circumstances.
> being readily available
I think under most circumstances shared cars will actually be more "readily available" than a car you own. Once autonomous ridesharing services reach a certain level of market penetration, it's practically guaranteed there'll be a car less than a minute away whenever and wherever you call for one. Plus there's no need to worry about where you parked, whether your car is out for repairs, or whether you can drive home without leaving your friend who hitched a ride with you on the way there stranded without a vehicle.
> lower cost of owning
Wouldn't a shared vehicle actually cost less, since the cost is split among all the different people using it?
> reduced insurances
Again, probably be cheaper with shared vehicles, since the driverless car company can self-insure.
> customizations
Yeah, this you'd probably lose with shared vehicles. No more bumper stickers or vinyl wraps. Though there may still be a way to pick a car of a specific brand or paint job if you so desire.
The cost of owning a car would be at least thrice what this service costs. A loan on a new car starts at almost $400 a month. The electricity alone would cost a private individual around $100.
The inconvenience of having to find a car and being unable to keep it for extended periods is real and may be enough reason for many to want to own a self-driving car, but the cost of owning is certainly higher.
Even with self driving vehicles, America will still have terrible traffic. If anything, self driving vehicles will make things even worse, instead of America finally fixing its broken/non-existent mass transit system.
I wrote about this a while back. Basically even if you only had self-driving vehicles on an interstate, all of them filled to 4 people each, travelling at 120km, you still couldn't even get to the fraction of the capacity of a single rail line running at 5 minute intervals:
http://penguindreams.org/blog/self-driving-cars-will-not-sol...
Also, cars are status symbols. Everyone has a phone with a clock on it, but watches still haven't disappeared entirely. Going driverless won't suddenly convince everyone to stop liking their cars and prefer generic Uber vehicles.