Not an expert, but I hear that one of the effects has been to slow down innovation.
Because a newly designed plane (with a rescue parachute, and a modern engine) is so much more expensive than one from the 1950s (leaded gas, possibly with grandfathered certification) everyone keeps flying the old ones. Cars have had many iterations on safety since the '55 Chevy, but planes not so many.
The whole FAA/EASA cert process is burdensome, but it is worth noting that the aviation industry has an impressive safety record. It is not at all comparable to the safety of a '55 chevy.
_Commercial aviation_ has a stellar safety record. The safety record for private and general aviation flying is pretty atrocious, and non-airline commercial operations (part 91, part 135) have varying levels of safety somewhere in between.
I think there can be little argument against the assertion that modernizing the general aviation fleet would improve safety. The majority of GA aircraft are using 60's technology carburetted reciprocating engines and running on leaded gasoline, and the cockpit is mostly analogue gauges with mechanical vacuum-driven gyros. Every car manufactured since the 90's uses fuel injection, yet GA pilots still need to worry about carburetor icing. That's not even going into other modern safety improvements like digital autopilot or ballistic recovery parachutes.
Because a newly designed plane (with a rescue parachute, and a modern engine) is so much more expensive than one from the 1950s (leaded gas, possibly with grandfathered certification) everyone keeps flying the old ones. Cars have had many iterations on safety since the '55 Chevy, but planes not so many.