Everywhere? You can't make generalizations like that, because there isn't a global trend. In developing countries, demand for car ownership is up, because of increasing affluence and the poor state of infrastructure in those countries. In developed countries, demand for car ownership is down, because of halting suburbanization, increasing awareness of expenses and externalities of car ownership, and availability of comparable alternatives. This is most apparent in Europe, but the long-term trend is downward in North America as well.
As for your analogies, they do not seem very apt. A major benefit to cell phone ownership is the ability to be contacted by or to contact people at any time, which a payphone does not provide. A major benefit to washing machine ownership is the ability to do laundry without schlepping your heavy clothes three blocks to the laundromat. The major benefit to car ownership—point to point transportation, on demand—would be provided by a competent robotaxi service. It won't kill car ownership, but for a significant number of people, robotaxis would provide everything they need out of a transportation, at a fraction of the cost.
Contrary to what you've been stating, there is precedent for replacing goods with services. Quite recent precedent, in fact. How many people do you know who subscribe to a service like Netflix? Of those people, do you think their consumption of DVDs (and, prior to that, VHS tapes) went up or down once they got Netflix? What about music: How many people are buying physical CDs these days, do you think, compared to in 2000? Sometimes a centralized service is superior, sometimes it isn't. The market will decide.
Between car ownership and robotaxis, I know which one I'd choose. There are a lot of people in this thread who agree with me. I think your "I don't know, everyone?" is entirely unjustified and I think you're vastly underestimating the frustration and expense involved in car ownership for a large number of people.