When the PFDs are changed (as per A380) to provide conclusive evidence of where the side-stick is, who has got control, along with rudder pedal position and AoA indication - then the "big red button" will be redundant.
mm43,
Correct me if I'm wrong, but I don't think it is how the 380 is equipped ?
To me it is more the kind of Animation you can obtain from FDR data.
What is seen as "big red button" is a simple way to force Direct Law and benefit from a more 'conventional' aircraft.