Loss of pitot tubes only implies loss of air velocity indicator. The attitude indicator, the altimeter and the thrust levers worked fine. I still can't believe they intentionally reduced thrust and pitched up for an extended amount of time, and not only thought this was a good idea, but didn't crosscheck the most fundamental instruments to confirm that the plane was flying level. And then proceeded to ignore stall warnings and stick shaker.
The human error was so severe that I'm not convinced that better alarms could substantially mitigate. At the end of the day, if a pilot forgets how to fly a plane, then their peer (presumably still capable of independent thought) needs to have the presence of mind to take over.