You make good points that are relevant to a lot of accidents, but in my opinion that is not what happened here. This was not a case of the automatics being faced with a problem and throwing control back to the pilot (who couldn't handle it), it was a case of the automatics actively putting the aircraft into danger by pointing the nose at the ground. It wasn't even a case of the pilots not paying enough attention to how the plane was flying or not understanding how to fly, they knew that they had a problem but they didn't know the steps to resolve it.
Boeing's reluctance to endanger the $1 million "no retraining" bonus caused them to make the unforgivable decision to not even mention that it was a possibility for the automatics to do something different than the NG. After thousands of posts here we have come up with the procedure that the pilots should have followed (the "Goldilocks" solution of turning off the electric trim , but only after using the electric trim to get back to neutral). Initially I thought of this as a case where the engineers did not have enough imagination to consider this scenario, but apparently it was well discussed at Boeing, so they could have had a procedure outlined for the pilots to follow -- but that might have involved retraining and thus losing $1 million per plane. They could have used two sensors (which is still not a good enough solution to defeat Murphy) but for unknown reasons they decided not to.
The fundamental problem is that Boeing turned an AOA failure from an annoying problem that the crews could have easily handled into a "do the right thing in 40 seconds or everybody dies" sort of situation. The first aircrew certainly had no idea what peril they were in; the same situation on the NG would have presented just as many flashing lights and stick shakers (as I understand) but would have been an otherwise uneventful flight and the pilots would have had a great deal of time to resolve the annoyances. The Max in the same situation pointed its nose at the ground and opened up a whole Pandora's box of interesting issues that the pilots were expected to solve with no help from anybody in a very short amount of time. Designing the automatics to do that with forethought is equivalent to designing an electrical system that you know will catch fire in some circumstances but assuming that the people in charge will know how to put out the fire.