That is certainly possible. There is also a flip-side. When there is a mixture of computer-driven and human-driven cars on the road there will be accidents. Most of those will probably be caused by the human drivers. Importantly this will be provable because the computer-driven cars will have telemetry to prove it.
So I think the question is will there be enough wins for computer-driven cars before a major systems failure tips people against them?
All great ideas are controversial, or have been at one time.