In "normal mode" the computer will not let pilots stall the plane, whatever they do; it will accept the commands up to what it considers dangerous. There's an "envelope" of acceptable plane movements; pilots can move inside this envelope but not outside of it.
In "alternate mode", the envelope is much wider and you can actually stall the plane.
If you're in normal mode, it makes sense to pull the stick all the way so that you're at the edge of the envelope: you climb as fast as you possibly can (as fast as the computer will let you).
And you can probably fool yourself when the stall alarm rings: the computer is telling me I'm near stalling -- I'm at the edge of the envelope, THIS IS WHAT I WANT!!
In fact you're not in normal mode anymore, and the computer is telling you that you're way past the envelope. But you can't register that, because for you that is simply impossible.
If that's what happened, the cause of the crash is insufficient training in alternate mode.
But to me the bigger problem seems to be that such an important change in the plane's behaviour could happen without anyone noticing. I'd consider the mode to be something the pilot must be made aware of, not something he has to deduce from the fact that the airspeed isn't available.
Perhaps the mode is shown prominently and the pilots just didn't notice it in their state of panic. Making it more prominent probably leads right into an insane arms race - the stall warning was as prominent as anything can be and still got ignored.
I don't envy the person who has to design a airliner cockpit's user interface and decide which of a hundred potentially vital pieces of information should be displayed how.
In the flight recorder log, at 2h10m05s, there was an audible "cavalry charge" alarm that indicated to everybody in the cockpit that the autopilot was disconnecting (plus message at the same time on the ECAM).
Then, on the ECAM message console 1 second later, the message "F/CTL ALTN LAW (PROT LOST)" was displayed: alternate law, protection lost. At the same time, Bonin said "I have the controls", which to me indicates that he knew that the autopilot was off and that alternate law was engaged.
 Page 45, http://www.bea.aero/docspa/2009/f-cp090601e3.en/pdf/f-cp0906...
 Page 88, Ibid.
If that's not the case, and the stall warning sounds even when there's no real danger of stalling (because the controls are operating in normal law), I feel like that's a terrible user interface.
If the flight computer is having to intervene and change the flight controls, then at the very least there should be a force-feedback mechanism in the stick which tells the pilot he's doing something wrong, and that he really shouldn't be yanking back the stick that hard.
The other bad part of the user interface is that the two sets of flight controls are not linked, like they were in the old days. With side sticks, it is not easy to see what the other pilot is doing. And averaging the control inputs of the two pilots is INSANE, in my opinion. Only one pilot should be flying the plane, and it needs to be quite obvious who that is at all times.
The CRM mechanism to take over flight controls should not be saying the words "I have control", it should be flipping a big switch on the center console that visibly indicates who has control.
However if you add force feedback of the plane computer "correcting you" you'd never know if it's plane or an another guy. Therefore, force feedback from the computer doesn't sound to me as a good idea. Some kind of feedback would be a good thing, but in panic, it wouldn't be noticed. I guess I'd put something like something "protruding up" on the stick when in another mode -- you'd feel and see it.
Finally, switch flipping is unnecessary if you have a force feedback. It think that's really the major feature missing!
Once your instruments start failing left, right, and centre you should go into what I call "advanced free fall" mode, check horizon (true, false or otherwise), check altitude, check parachute, repeat... If you hit gimbal lock (or similar INS failure) in the dark, well just bend over and kiss it goodbye.