You have provided a good illustration and while technically your argument is correct; I consider it to be somewhat irrelevant. There are so many variables that even with all of the theory, engineering and testing... it is still not possible to predict every scenario that a pilot can get an aircraft into.
When I was taking spin training. I asked the instructor what would happen if I didn't take the proper corrective action. She was an award winning aerobatic pilot, but she admitted that in the plane we were in that she didn't know. One would reasonably assume that the plane would keep spinning until it hit the ground. Actually in the aerobatic plane we were flying... after rotating half a dozen times the plane picked up enough speed to start flying again and we had actually lost less altitude than we did when using the proper procedure.
It is possible that another student and instructor in the same plane who weighed less than we did could have tried the same thing on a hotter day and the plane might have gone into an unrecoverable flat spin. It is not very likely. I would be careful about speaking in absolutes when discussing aviation. For what ever reason the crew was not able to recover from the situation they placed themselves in. I hope that something can be learned from this situation that will help avoid future tragedies.
One will notice that almost all jet transport aircraft will have takeoff range that the horizontal stabiliser is effective over, not having the horizontal stabiliser set in this range for takeoff could make the elevator potentially ineffective, hence it is an item check during the walk around and pre takeoff.
Keep in mind that ACARS messages are not sent sequentially when problems are reported, but according to a priority logic when multiple messages hit the que at near the same time. Folks with detailed knowledge of the A330 systems have said they expected several additional messages to have been received based entirely on those actually received.
The last being presumed to indicate that the fuselage had broken apart until the evidence recovered from the ocean showed that the oxygen masks had not deployed and there was no indication of decompression. It is this last message that provides the basis for the assumption that the entire event took 4 minutes. We don't know that.
It is now assumed the last message indicated the aircraft was descending with such negative vertical velocity that the pressurization system was unable to equalize cabin pressure quickly enough.
The aircraft acknowledged receipt of a verification message of the last message about 2 seconds after receipt - there was no further communication (The ACARS transmission process included four back and forth verification hand shakes between the receipt center and the aircraft).
We also know that one gap in the nessage sequence of approx 31 seconds was due in part to the difficulty of maintaining reliable satellite communications by the automated systems. It is assumed that additional messages were in the transmission que by never sent due to abrupt termination of the event that occured.