The challenge with measuring the safety of general aviation is that it is much more behavior-dependant. All of the US airlines use the same standards for deciding when to fly/ not fly for weather, have similar maintenance programs, training requirements, etc... When it comes to private air travel, it's all up to the pilot and the insurance company.
I imagine GA follows something like a Pareto distribution, with 10% of the pilots involved in 90% of the incidents. That 10% would get retrained or weeded out in the airlines, and the rest get much more consistency on all the rest of the stuff you mention.
So yeah, there really isn't any one "the safety of general aviation." It's a huge spectrum.
Another challenge is reporting. The FAA knows exactly how many flights and how many hours the airlines did last year, but GA activity is much harder to gauge. It's hard to figure out what safety looks like when you don't have a good figure for the denominator.
From my limited experience working with them, the general aviation insurance industry seems ripe for startups. Data science is a huge deal in insurance, but the companies insuring Cessnas and Pipers don't seem to have fully caught on.
