I can understand the intent to minimize altitude loss when recovering from stalls, but the Air France pilot didn't even start trying to recover from it--he kept pulling back on the stick even after the stall alarm started going off. It doesn't seem rational.
It wasn't rational at all - it was grossly bad airmanship. I used to hold a PPL, and my father was an RAF fast jet pilot, and the Air France pilots made a huge number of errors that compounded themselves to cause the crash. There's an adage, which is usually true, that most air crashes - especially where pilot error plays a major part - require a long chain of errors/mishaps to congregate in a "perfect storm" in order for a crash to happen. Of course, not many people ever hear about the numerous times where a shorter chain of errors/mishaps take place which don't result in a crash. But there are a lot of such events.
In this instance, the two junior pilots seemed to make two extremely serious aerodynamic errors that were the genesis of the eventual crash. Firstly, they failed to understand or apply the basic knowledge that when flying at high altitude, the thinness and oxygen depletion in the atmosphere mean that three of the four forces acting on the aircraft - lift, drag and thrust - are increasingly diminished, while the fourth force - gravity - remains constant. This of course has an increasingly dramatic effect on the way in which one should pilot an aircraft at high altitude. Failure to understand/this principle appears to be the main reason why the pilots manoeuvred the aircraft into a nose-up descent and stall (including, unbelievably, the apparent fact that they flew the aircraft to the limit of its altitude envelope, in a misguided attempt to overfly the weather)
The second basic aerodynamic error the pilots appear to have made is to have egregiously failed to apply standard stall recovery procedures. Regardless of the (temporary) failure of the pitot probes, the pilots should have been under no illusions that they were in a stall. And whether or not they thought that a FBW Airbus was technically incapable of stalling, the stall warning should have instinctively caused them to disengage the autopilot (assuming they thought it was still engaged, although in fact it had disengaged after the pitot probe problem) and perform a manual stall recovery. As plenty of others have already pointed out, if they had pointed the nose down and increased thrust, they would have recovered from the stall within a matter of seconds (depending on the altitude at which they started the recovery). Indeed, had the pilots simply taken their hands and feet off the controls, it's highly likely that the aircraft would have corrected its stall all by itself well before any threat of a crash.
Aside from these two errors related to aerodynamics, there also appear to have been serious errors in communication and CRM, and there may have also been errors in the way Air France trained its pilots to fly these aircraft. But I'd argue that regardless of these other "soft" factors, the shockingly poor airmanship of the pilots was the overwhelmingly major contributor to the crash. I'd argue that someone who'd had four basic flying lessons (and not even a licence), if they had been sat at the controls of that aircraft at the start of the problems, should (and would) have been able to fly the aircraft safely.
As a slight aside, my father was involved in many RAF boards of inquiry into military accidents, but he also had a few former RAF friends who worked for the UK Air Accidents Investigation Branch (AAIB), which investigates civilian accidents. One of my father's good friends was involved in many high-profile investigations, including PanAm 103, Kegworth, and - most notably for him perhaps - the British Airways BAC11 accident where the windscreen blew out, sucking out the captain, who was saved by other crew holding onto his feet and landing the aircraft safely. This incident was featured in an episode of "Mayday" (re-titled "Air Crash Investigation" over here), and my father's friend - Stuart Culling - was the AAIB investigator who cracked the case by using human factors to establish that sloppy (and too time-critical) maintenance procedures had led to bolts of the wrong size having been used to reattach the windscreen during maintenance.