For the vast majority of people who own a car, continuing to own the car will remain the better deal. Most people need their car during "rush hour", so there isn't any savings from sharing, and worse some people have "high standards" and so will demand the rental be a clean car nicer than you would accept - thus raising the costs (particularly if you drive used cars) Any remaining argument for a shared car dies when you realize that you can leave your things in the car, and you never have to wait.

For the rest - many of them live in a place where not enough others will follow the same system and so they will be forced to own a car just like today. If you live in a not dense area but still manage to walk/bike almost everywhere (as I do), renting a car is on paper cheaper the few times when you need a car - but in practice you don't know about that need several weeks in advance and so they don't have one they can rent to you. Even if you know you will need the car weeks in advance, sometimes they don't have one when you arrive.

If you live in a very dense area such that you almost regularly use transit (but sometimes walk, bike), but need a car for something a few times per year, then not owning a car makes sense. In this case the density means shared cars can be a viable business model despite not being used very much.

In short what you say sound insightful, but reality of how cars are used means it won't happen for most car owners.