The rational fear is of automation introducing systemic failures. Imagine a "flash crash"[1] type event applied to widely deployed self-driving vehicles.
I never understand why it has to be either one or the other. Either we accept deaths caused by human drivers, or we go full autonomous and we accept deaths by software errors.
The way I see it, AI assisted driving is the way to go. Fully autonomous driving is, at least in my opinion, a pipe dream. No amount of testing will ever be able to prove an AI is safer than a human in all situations. They might be safer in some though, e.g. highway drives, quiet roads at night etc. So instead of pouring in vast amounts of money developing fully autonomous vehicles, why not spend it on improving the existing AI assistance features that already exist, so we can prevent most human errors, without introducing new AI failure modes.
Note that this means we should all forget about the dream of not having to pay attention on the road because 'the car drives itself', and that we should actually dial back things like Tesla autopilot, which venture too close to 'car drives itself'. The driver should be in control, until he/she makes a mistake, then the AI should prevent worse.
On a side note: people comparing plane autopilots to point out the merits of fully autonomous driving are really missing the point, there is no AI in avionics whatsoever.
I do think we'll get to fully autonomous for some significant useful subset of driving such as paved public roads and can probably do things to help out the AIs with corner cases (beacons, etc.). That said, I actually agree that the last 10% that gets things to reliable Johnny-cab level are probably a lot further than many are assuming. Given the level of investment and advances that have been made I'm probably even more optimistic than I was, but I still think it could be 30-40 years before you can order a robo-Uber in Manhattan.
Yet, Robots and automated machines (not the autonomous vehicles) still killed/injured a few dozen people since 1984 according to U.S. Department of Labor. [1]
You said we won't accept those deaths "even in the single digit", not 40k+ deaths, which is a few orders of magnitude higher.
Also I don't understand why we would accept freak accidents but not other accidents? An accdient is an accident. A death is tragic regardless what caused it.
We don't accept the robot deaths. Any time one happens people scramble to "make sure this never happens again". When someone dies in a car accident, we yawn.
[1]: https://en.wikipedia.org/wiki/2010_Flash_Crash