@Confiture
Well of course the elevator doesn't have an intention to deliver anything; it is merely the servant of the control laws. So far as those are concerned the behaviour is not really surprising - you should read the Bilboa report where it says:
Additionally, in these high angle of attack situations, with a tendency towards phugoid movement, studied by longitudinal stability, in which the aeroplane oscillates between two kinetic and potential energy levels, the EFCS behaves as a damper of the oscillations, commanding appropriate variations of angle of attack in a way that, when the aircraft is slowing down, makes it pitch downward and vice versa,"
IIRC in the Habsheim accident, the aircraft was still losing speed up until one second before collision with the trees. Although higher power had been commanded, it was simply set too late to arrest the deceleration and remove the damping correction in time for pilots demand for higher AOA to be satisfied safely and in time.