the probable cause of this accident was preoccupation with an inflight malfunction and failure to monitor properly the airplane's flight instruments which resulted in losing control of the airplane.
The flightcrew's statements about the ADIs failing were not substantiated by the facts. It is most likely that the flightcrew became spatially disoriented during the upset.
They were unable to believe the information displayed on the ADIs, did not recognize the unusual attitude of the airplane, and were unable to take the correct action to recover the airplane until it began to emerge from the clouds.
The increased automation has not necessarily reduced pilot workload, however, but has shifted it to monitoring tasks which the pilot formerly had to perform, and there is evidence, from both research and accident statistics, that people make poor monitors.
Research also indicates that the excursion from a stabilized condition might be exaggerated even after a system anomaly is detected, because of the period required for a pilot to transition from system monitor mode to system controller. Time is needed to "ascertain the current status of the airplane and assess the situation," 13/ before the pilot can reenter the control loop and take corrective action.
The above is not a new AF447 leak or even Airbus related. It is from the 1985 NTSB report on the China Ailines 747 loss of control initiated by a single engine failure at altitude. (my bold)
China Airlines B747SP Loss of Power and Inflight Upset
Fortunatly they did break out of clouds in time to recover, although with some injuries and extensive damage.