After reading this thread, I'm left wondering if every large passenger aircraft should not have a large (10cm diam.) knob at the centre top of the panel labelled "I Have Control!".
Pushing it in would de-activate all the automatics, except those needed to enable the pilot to fly the aircraft manually, ie stick 'n rudder, throttle and flaps, to somewhat over-simplify it.
I have sat in the Concorde jumpseat during an approach and landing with the FO flying it manually using just those controls. (The trips round regional airports were mostly to give crews the minimum handling they needed.)
I was there when, still sitting in the flight deck at Muharraq , the Captain of a B707-338C, operating as QF739 on February 21, 1969 explained how he regained control after the aircraft went out of control over the Arabian Gulf on route to Bahrain at FL350 and M 0.81, dived inverted, rolled, probably went supersonic momentarily (not recorded accurately due to compressibility issues at the pitots) ) recorded +4.57G and - 0.63 G, and lost 19,000 ft.
"I realised that we had finally entered a spin", he said, "so I recovered it like I would a Tiger Moth. No big deal." And off he went with the crew for a stiff drink in the Gulf Hotel. We found soap stuck to the ceilings in the toilets.
Crews would be trained to recognise a situation where they have lost effective control of their aircraft because they do not understand what the automatics are up to, and/or when something is obviously seriously wrong and getting worse, and to use the button to recover, stabilise, whatever, using their basic flying skills, if they have any.