You really cannot blame the crew.
They experienced (i.e. quietly slipped into) a pitch-up (and thrust-) induced, and very insidious, deep-stall entry at high altitude - a straight unapparent and unremarkable entry into a very high descent rate, featuring a quite misleading and almost normal pitch attitude.
Sorry, but that response may be valid for the first 15 seconds, but not the last 3 minutes. The pitch attitude was definitely NOT normal or even "almost normal" with 10+ deg nose up at 30,000'+!
The Airbus software may have contributed to the confusion with the on-again, off-again stall warnings, but an experienced pilot should have recognized the reality within a minute or less by the attitude and [lack of] airspeed.
Another thought just came to me...
What would have happened if the pilots just took their hands off the stick altogether. What would the computer have done? Has anyone tried this in a [lab] simulator?