So how will this work when none of the instrumentation is giving the computer the correct airspeed? IN the Air France crash, all three of the Pitot tubes had failed.
Worst case, add power, level out, and hopefully you'll be stable for a few minutes while the pilots catch up to the airplane.
That said, I'm not an aeronautical or control systems engineer, so this is just speculation.
Once you get to airliner altitudes (say, FL350 and above), the plane does not really want to fly anymore; there is only a narrow band of throttle / pitch inputs that will result in stable flight. You can see this in your favorite flight sim: take a Cessna 172 up to 4000ft and try crashing it. Turn off the engine, cross the controls, and pull the nose up until it stalls. Then release all the controls, and the thing goes back to flying normally with no input from you (and without an engine). Then try this again at 13,500ft in a thunderstorm and see what happens. You can even have engine power. The plane behaves very differently at its service ceiling.
Airspeed data is critical, which is why there were three redundant airspeed systems. Turns out, it wasn't enough.