Also, it seems like regulated utilities have been more effective at providing essential services widely at low cost than large private oligopolies such as cable and wireless, so I have no particular desire for an Uber/Lyft duopoly.
You aren't likely to want to own your own self-driving car in a major city, unless you're an eccentric rich person, or a car hobbyist, or a old fogie. Urban garage/parking space is expensive for an asset that's idle 22+ hours of every day, and fueling/maintenance/looking-for-parking are likely not the best marginal use of your time.
What's your dislike of "something used by tens of thousands of unknown people", as long as it's well-maintained? Do you avoid libraries, sidewalks, parks, airports, shops, and restaurants?
Right now, Uber and other transport-network-providers are becoming "people I know and trust", because their systems have consistently delivered quick, clean, reasonably-priced rides across many times/places. App-dispatching a suitable-quality autocar from the nearest competitive local provider is going to save a lot of time/energy/pollution, compared to coordinating loaners from friends/family.
If transport regulators like city councils and taxi commissions were better at this sort of thing, they'd have bootstrapped a similarly rapid and ubiquitous ride-service years earlier, using their unique governmental coordination powers. Instead, they let a patchwork of inferior alternatives fester for decades.
I'm not sure of the eventual market structure of autocar-dominated city streets. Automation and standardization might make room for many providers, or just a few. Regulators could easily screw things up, by locking in specific practices or incumbent providers based on early guesses, biases, and corruption.
We'll just have to let lots of things be tried and see what works. For rapidly exploring the possibility space, the vigorous investor-fueled competition we're seeing now is very helpful.
I own my own home, means of transportation, eat most of my meals at my own table...the idea of being a renter of all the major environmental necessities of life is simply not appealing to me in the slightest. I'd rather sleep in my own natural latex, bed bug free bed, and sit on my own sofa or read a book on my own chair, call me crazy. There's never sticky goo on mine, or weird smells. I like private ownership.
For me, Uber is the opposite of "people I know and trust," and I have no desire to have them monetize my movements.
First it will be the occasional users or those with a second car or on a budget, but eventually most of us will either pay per use or have an account for regular use rather than outright buying a car like we do now.
For commuting, many will be taking shared vans (possibly pod-based) that pick an efficient route rather than plying a typical bus route.
And we'll get the vehicle we need when we need it. You won't take a ute to dinner with your partner. You won't have a three-door hatch when you need to choose and bring home large items, or transport the family on a road trip.
The future Uber won't even be people you know or don't know. It will be a driverless car.
Self-driving cars-for-rent will get you places both faster and cheaper than possible in your own car. That could make private car ownership seem quaint or even ostentatious in most cities.
Rental cars carry costs that I don't have with my own vehicle: frequent transactions, additional liability issues, wasted mileage driven between fares, uncertain transit times, daily cleaning and inspection for damage, commercial licensing and insurance, middle men, management, marketing, accounting, additional taxes, regulations, and covenants. If I leave something important in my car, it's still there the next day. I don't have to worry about vomit in the backseat. I don't face a transaction cost and a delay (or the uncertainty of a no show) to go to work, to drive home, to hop in the car and go to the mall, or grab a bite. I can leave things in my car. I have less exposure to pathogens and pests from surfaces in revolving contact with thousands of strangers from all over the world, lower probability of exposure to cold and flu viruses, fewer vectors for bedbugs to travel into my home.
I can't see rent seekers (esp short term ones) being so far under my costs that after adding their markup, it will be particularly cheaper for me. The 5 year TCO for a Prius (staple of the ridesharing industry) according to Edmunds is a little over $18 a day at 41 miles per day, 44 cents/mile inclusive of insurance, gas, maintenance, etc. The average fare mile on the Peninsula for a cab is $3. I don't see ridesharing companies finding an order of magnitude in efficiencies and still delivering any kind meaningful profit.
Maybe private toilets will seem quaint and ostentatious, and we'll be soon freed from the tyranny of private bathrooms by happier times of public lavatories.
