Not necessarily. Part of the freedom is that you don't have to have a destination in mind. You can simply drive to wherever you want, whenever; you can explore. This also does not mention issues about surveillance, corporate control, privacy, etc.
Driving provides a very real sense of freedom and power to people that they may not find in many other aspects of their life.
Most people will also remember being teenagers and having their parents controlling the keys.
Autonomous cars are like going back to being a teenager except now the government or some corporation owns the keys and tells you what is allowed.
Tech people don't always think about these things but they will have a major impact on how the technology is adopted or not adopted.
Additionally, I just think we'll have to see about that later part. For me the freedom is freedom of transport, the cars are just an expression of that.
Yes, people will be skeptical of shared self driving cars, but to suggest the problem is the self driving aspect seems a bit off.