The other big factor is the construction. Cars are largely stamped and then welded together. Aircraft are either stamped/milled aluminum that is then manually riveted together (production volumes are orders of magnitude lower than cars so no robots are used) or they are made of fiberglass/carbon fiber composite which is even more labor intensive to form. The issue with the comparison with cars is that they're way cheaper than they reasonably should be because of the sheer volume that they produce. In the time it takes cessna to build one plane, ford can pump out 1000 new cars.
In my humble opinion, the FAA does a lot more than an air regulatory agency should[0].
Since plane crashes are rare enough, the government litigates against everyone who ever worked on your plane if somebody ever dies in connection with it, and unless you can prove it was user error (expensive in its own right), you will end up paying millions in settlements and process. These costs are added at every level of the supply chain.
The FAA process could seem to make aviation safer if aviation technology never had to change ever again; but because there is so much to be done in private aviation that won't ever be done because of the cost of certifying craft with new technology; there's a good chance that safety devices have been held up by the process as well.
[0]: https://fee.org/articles/how-the-faa-brought-down-uber-for-p...
Roughly, they consider these groups, from lowest to highest priority in terms of keeping them safe:
1. Pilots. These are the lowest priority because they're the most in control and best understand the risks. If a pilot wants to turn himself into a red splat, that's his own concern.
2. Knowledgeable passengers. These are people who may not be pilots but understand aviation to some extent and have an idea of what they're getting into. They can't necessarily evaluate all the risks completely, but they can do a pretty good job of it. The FAA can't directly determine this, of course, but they use "for hire" as a proxy: if you're just taking people for fun or as a favor, it's assumed they have some idea of what they're getting into. If they're outright hiring you to fly them around, it's assumed they don't.
3. Passengers who are random members of the general public. Most of these people know little about airplanes and about the risks. They can't be counted on to evaluate things for themselves. People paying random pilots/companies to fly them around are assumed to be in this category. (And people buying tickets on a regularly-scheduled airline flight are assumed to be even more random than people hiring a charter, for example.)
4. The general public on the ground. These people aren't even involved in the process and have no choice in the amount of risk they're exposed to.
This is why the requirements get steeper as you move from recreational flying to commercial flying. If you want to fly solo over empty land, they don't care too much if you get yourself killed. If you're going to carry a hundred vacation travelers who just want to get to the beach, things are more strict.
(And I don't know that it is actually hard to find ones doing it now. Certainly the airlines are almost ludicrously safe, but the context here is GA, where things can be much more lax.)
When people get upset about the FAA's safety stance in GA, it has less to do with the part 61/91 regulations (airman certification/operating procedures) and more to do with the equipment certification standards. A common example is the reliance on vacuum driven gyroscopic instruments when MEMS technology provides better performance with a much lower probability of failure. Up until recently the FAA made it almost impossible to retrofit old aircraft with generic glass panel systems even though these systems provide vastly greater safety margins when used correctly. I personally have experienced a vacuum system failure, but luckily not while in IFR conditions.
Beyond instruments, the bulk of the fleet of 30-50 years old and beginning to show it's age, but it's prohibitively expensive to certify new designs that incorporate more safety features like CAPS (parachute systems), composite energy absorbing seats/fuselages or digital engine management systems. We're also still entirely reliant on leaded fuel (100LL) due to cost hurdles in certifying engines that can run on JetA or anything else for that matter.
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