The vane requires airflow over it to give accurate readings,
Does it? How about a system where if it is
not giving a reading within 16°AoA, it signals a stall? Say it is pointing "to the ground" whilst the aircraft is airborne. What do you reckon the crew needs to know? That aircraft isn't flying ie it's stalled. It doesn't matter where the vane is actually pointing.
But in this case, just when the crew needed the most "reminding" (and who would have not been confused: VSI off the clock going down, but with speed tapes on nothing, "knowing" that only a couple of minutes before they were giving duff gen), the stall warning silenced. Had it kept screaming at them, maybe their confusion would have eventually been overcome and one of them would have stuffed the nose down to recover the thing.