It has to be appreciated what kind of stall they were in. As stated in one of the early threads, the aircraft does not enter a 'true deep stall.' However, their flight profile, the feel, and basic instrument readings could have certainly given that impression to the average line pilot. The major difference would be, for a limited time/thousands of feet, they weren't trapped, as in a deep stall.
The incredibly powerful instinct to pull away from the ground - as suggested above - is I'm sure, very real, and to get another warning, when for a moment you do the right thing, must have bolstered that faulty reasoning considerably.
It probably wasn't long before fear affected the pilots' normally methodical reasoning. It's almost certain to be the case not long after their inflow of data became confused. Their situation must have seemed almost surreal in the latter stages. That is pretty solid psychology. Not a good state to be in when you need to willfully force your hand to obey an absurdly counter-intuitive command.
There are a lot of people better prepared now, as a result of this tragedy.
Pitot heads:
They're expensive, vulnerable and need complex translation before their data is displayed. They wouldn't have been there all these years if there was an easy alternative. However, I'm surprised there isn't a backup system based on alternative technology.
Air particles, and especially water droplets can be detected electronically and this used to measure speed. The trouble is, all the same ice issues apply, with the electronic detection being far more sudden in the way it fails.