PJ:
I will defer to your deeper understanding of this flight problem set.
I will offer, as a point related to training, that since airspeed is an imbedded element of an instrument scan, and a critical performance measure in any instrument scan, the unexpected lack of it disrupts the scan. The "don't pay attention to the airpspeed" scan is a non-standard scan, and (IMO, I am biased due to some years of training pilots) should be practiced so that the PF is flying and crosschecking while deliberately ignoring a fundamental scan item ... while the PNF is doing as you illustrate, and handling the trouble shooting.
EDIT: I don't think I need to tell any experienced pilots this, but for those who aren't -- if you don't practice and use your instrument scan habitually, it tends to start off a touch slow when you begin to use it at need. Also, if you don't practice your degraded mode scan, your scan will tend to be slow (initially) when you need to implement that scan pattern. How much time did this crew have to get into that rhythm? Don't know.
This I have seen first hand, not only in my own flying, but also in hundreds of other pilots, when I gave them instrument checks or was being the SOB at the console for a simulator training event intended to "run them through the wringer." This observation applies to both inexperienced and experienced pilots. How quickly the scan, or degraded mode scan, was established, or re-established, varied with the pilot.
I grant you that crews in some other events where AS became unreliable (under other conditions and variables) were able to manage that transition via one means or another. Based on the points you raise, unreliable airspeed wasn't a new failure mode experienced for the first time by AF 447's crew. What it may have been was that rare failure mode, experienced with some novel other conditions, and most likely for the first time by that crew. (This consideration is related to the question I asked to studi about what Conventional Wisdom is and was among the A330 pilot community in re his described escape maneuver ...)
Friday will hopefully be enlightening.