The problem with this scenario is that modern cars are already safe enough that it will literally take decades to gather enough data to prove a statistically significant 10% safety increase from autonomous cars, even if you sell millions of them.
Keep in mind the NHTSA safety statistics you frequently see quoted are for the entire car population on the road, with a significant portion of 10-15 year old cars which are less safe than new cars. Even 25 year old cars without crumple zones and airbags is something you see on the road every single day.
Those have to do with fatality rates, not accident rates(1 accident per 250,000 miles).
>> statistically significant 10% safety increase
For a sample size of a million cars , each year is 15 Billion miles, i.e. 60,000 accidents per year, vs 54000 accidents per year is statistcally significant.
Fatality rates are what's recently been discussed, e.g. related to the Tesla AutoPilot crash.
If you switch to measuring "accidents", two big concerns pop up: 1) who defines what an accident is? and 2) if we get autonomous cars that end up in less minor accidents but same or more number of fatalities, is it really worth it?
We could extend it to "fatalities and accidents where someone is left permanently disabled", which is pretty unambiguous and does measure the most important factors. But I'm afraid (or rather, glad) that this won't give you an orders-of-magnitude increase in statistical samples as you get when counting all accidents.
Keep in mind the NHTSA safety statistics you frequently see quoted are for the entire car population on the road, with a significant portion of 10-15 year old cars which are less safe than new cars. Even 25 year old cars without crumple zones and airbags is something you see on the road every single day.