Sensory overload and no clear readout of what is actually broken (pitot tube icing in this case) is bad but the fly-by-wire joystick configuration is what really doomed this flight. In Boeing airliners and many other types of aircraft the control sticks are mechanically linked together: you can physically feel if the other pilot is fighting your inputs:
> “Controls to the left,” Robert said, still worried about their bank angle. Pressing the priority button on his side stick, he took control and locked out Bonin, but Bonin immediately pressed his own priority button and assumed control again.
If the controls were mechanically linked Robert would have recognized his inputs were being overridden and would have been able to save the plane.