I highly doubt that. What's way more likely is that even if they are just slightly more safe, you will be able to get cheaper insurance for them. Eventually, over time, this will push all self directed cars off the road.
There is even a disruption potential: Put together a new insurance company that only insures self driving cars and make it meaningfully cheaper. The ones that still insure self directed cars and self driving cars both will have a tough time to compete because their blended economics don't allow for the super cheap rates.
I don't think many people will necessarily own their own self-driven cars. Why have something there idle when it could be doing other work? More likely it will operate more like a taxi or by subscription. Or even own your own, but have it used in a pool to recoup costs, a bit like swap-n-go gas bottle refills.
There is even a disruption potential: Put together a new insurance company that only insures self driving cars and make it meaningfully cheaper. The ones that still insure self directed cars and self driving cars both will have a tough time to compete because their blended economics don't allow for the super cheap rates.