We still have people who buy
We still have people who buy and ride horses. I anticipate that there will be places where one can indulge the urge to be behind the wheel. You say that cars will become like refrigerators, with no value added. Are you saying that a plain vanilla refrigerator from home depot competes with a Sub-Zero? Really? Why do people buy Rolls Royces if they can rather than a Hyundai Accent? Will they cease to do so in an autonomous future?
My point is that there will always be a market for differentiation. I suspect this was the case in ancient Sumer and I expect it will be so until the Sun flames out or humanity snuffs itself out. Autonomy doesn't mean lack of differentiation, it means actually that everyone has a chauffeur of one's own. Private ownership won't be snuffed out, it may mean that private owners will use a Tesla app to "rent out" their autonomous Tesla and compete with Uber!
I rather think that your view of the future is rather dystopian. The logical outcome of the winnowing of car sales will be to free up income for toys we haven't thought of yet. Or maybe a trip to a space station for a week of zero-G! Who knows? I welcome the future. You should to.