Meet the most popular aircraft in history: https://en.wikipedia.org/wiki/Cessna_172
The only updates are new engines, the aircraft's control is not just analog, it's literally "planks moved by pulling on wires".
It seems to me that the problem here is that new airplanes are cost prohibitive. Your solution to light aircraft safety is to make the majority of light aviation illegal or too expensive to function, like solving the problem of unstylish watches by outlawing anything cheaper than a Rolex.
People seem to have the impression that GA has to be safer than driving, or safer than some other benchmark, before the safety level is acceptable. I am perfectly willing to accept some risk (the raw rate of fatality per ground mile is about 20x higher for GA vs. driving) even as a passenger, and I don't see why the FAA should be in the business of determining what risk is acceptable to passengers. I think the FAA's primary responsibility should be to the broader public, who experience the same risks on the ground regardless of how much or little GA they buy, rely on, or associate with.
Some of the FARs make a lot of sense in this regard, for example the rules for single-occupant ultralight aircraft (including powered paragliders), and ideally a similarly pragmatic approach can be applied to other questions in aviation regulation.
Oh wait ...