I am a little mystified about this "big red button", especially related to Perpignan?
The "big red button" was precisely what caused Perpignan! The AoA probes froze at a sensible cruise reading, and despite clear indications as such to the crew (illogical Angle of Attack displays on PFDs), they proceeded to test AoA protections.
Due to the frozen AoA probes, AoA protection did
not occur. The crew just carried on slowing down (PPL indication of approaching stall: 1), with a very nose high attitude (PPL indication of approaching stall: 2), to well below the speed
clearly written in the test schedule on the Flt Deck at which the test should be "knocked off".
In effect the frozen probes acted as "the big red button", and enabled, unfortunately, the crew to kill themselves
It isn't a particularly good advert for the "big red button" concept to me?