I agree with you. Job One is fly the damned airplane! Bells, horns, stick-shakers are warnings of impending problems or sometimes not. In this case, Boeing’s errors challenged the pilots, but it was the failure of the crew that caused the loss of life.
I’m typed in the 727, 737, 757 and 767 and instructed in the 737 as well as served as test pilot for AC coming out of maintenance. I instructed ATP’s for several years and also flew the line. No pilot that I instructed or checked would ever have failed to have disconnected the stab trim OR failed to fly the airplane.
And as an aside, can I point out that a triple autopilot, no-pilot AC would have come to the same end as the failed crews did. GIGO.