Because of economic realities, the entities that provide the "on-demand" vehicles will never have enough vehicles on hand to meet peak demand situations. Users will be forced to "car pool", so you might have your kids sharing a ride with a pervert or someone with a contagious disease, you might find yourself riding with a vomitous drunk. How would evacuations in advance of hurricanes or wildfires work out?
For some, reliance on on-demand vehicles will be fine, for others that will be unacceptable. Private ownership of vehicles will never totally go away, except by government edict.
Believe it or not, freedom of movement is important to many people, and is something to be feared by any would-be tyrant.
You make some good points. But...
Ride-sharing won’t be necessary.
Vehicles won’t need to be owned. And, the “rides” will be provided by fleet operators, but not by corporation such as Uber or Lyft. The fleet operators will be the carmakers themselves, since there won’t be any business needs for car dealers and manufacturers will have to operate their own vehicles in fleet formats in order to make up the difference in lost sales.
Vehicles will be summoned via phone or smartphones or PCs or even smart home assistants and perhaps smart TVs, and can be used on a scheduled basis, such as for a morning ride to work and afternoon ride back from work.
The whole autonomous vehicle future will be very disruptive, and it will affect car ownership (no longer available) and fuel-usage (much lower demand, if any), and cities and states and the whole country will have their complete roads and highways changed according to the needs and demands of vehicle usage. For example, no more parking lots, and no more parking garages at airports and no more home garages.
We’re in for a very disrupted future.