More to it than just pilot control inputs
I am a pilot and a software engineer. Back in April I posted about a scenario that turns out to be quite similar to what the FDR and CVR describe. In that post I suggested that the pilots would have applied TOGA and full nose up trim. I think it is eminently reasonable, given the pilots' procedures training, practiced in the sim, and their confidence in the FBW system, that the pilots applied nose up control inputs and full power. Don't blame the pilots!
I believe the fundamental cause was that the computers flying the plane used invalid air data inputs (altitude and airspeed) with pilot control inputs that were based on the assumption that the computers had valid air data inputs (altitude and airspeed). I believe the FBW was not designed or tested against this particular set of inputs. That is based on my software engineering expertise and not so much what I know about flying.