A little bit of knowledge is a dangerous thing:
The Habsheim A320 protected the aircraft too. The system knew better than the pilots then.l So it (the system) landed the aircraft against the pilots wishes !!! Protections ??? Yeh sure.
The aircraft was below 100ft so the A-FLOOR protection was not active and the engines in any case would probably still have taken too long to spool-up and provide the thrust to avoid the trees. The pilot was flying at 30ft instead of the briefed 100ft
What about the A320 that crashed into the Mediterranean with 3 airbus test pilots on board?
They omitted an item on the Air Test Schedule, as I recall, and didn't want to climb back up to the recommended safe altitude to carry it out so they checked the low-speed protections at an unsafe altitude (3000ft) with tragic consequences when they AoA probes froze due to water ingress. Had they been at 14,000ft which is, I believe, the recommended altitude for the check they would probably have recovered from the stall.