ZionGate –
You’re correct that private planes have a more frequent rate than commercial, but you’re not correct that they happen “quite frequently.”
You’re also incorrect that they’re underreported (at least to any significant degree). Not sure how you think anyone would avoid reporting an accident like that. Airplane mechanics document everything, and significant I jury or death is obviously documented.
More importantly, the vast majority of the accidents are due to errors (either during flight or preflight) that are somewhat negligent. What that means is that if something c”v does happen, it’s usually the fault of the pilot. That’s unlike driving a car where a person can be a very safe driver, but is often at the mercy of another irresponsible driver. That doesn’t happen often in the air.