Interesting question. Like you, I too believe that a large population may prefer Lyft/Uber type services instead of dealing with the concerns of owning one (e.g., parking, requiring space for parking, insurance, time spent in fueling, maintenance, etc.).

However, I tend to think that there still may be a decent size of population who'd prefer owning. Others mentioned the convenience of using cars for storage, being readily available, lower cost of owning, reduced insurances, customizations, etc. Along with these, I believe some other factors exist.

In context of self-driving cars, we typically tend to picture urban transportation first. However, there will still be needs for long distance commuting, or taking long trips for pleasure. There will always be places where people frequent less compared to major spots/suburbs in a city.

People may not always want to hop into a random car every time they take a trip. The cost/time involved in flagging a car of your choice may not be worth the effort for some. Also, keep in mind that many think of cars as a statement, another way of expressing their beliefs. Take for example, preferring German vs. American vs. Japanese, some prefer minimal space, others may like to exhibit opulence.

All in all, there will be a large shift towards not-owning cars, but there may always be a market for owning (at least for a long while).