Back in the days when the 737 was first introduced, designed for 2-pilot operation, BALPA resisted this strongly on the grounds that "
3 pairs of eyes is better than 2" during critical phases of flight (I was around that time working on BA's flight sim maintenance, having worked previously at Link-Miles building sims). The result was a "redesign" of the Trident, which was originally planned to be a 2-pilot aircraft, and the solution for BA was to introduce "P3" and move much of Trident's (previous Flight Engineer's) fuel and systems instrumentation (IIRC) back to the rear right side of the flight deck.
The problem of "pilot suicide" was not an issue then and neither was the much more recent terrorist issues that resulted in the self-destruct intention of a pilot enabling him to isolate the flight deck in order to carry out his suicide, and the resulting deaths of entire aircraft.
Reinstating the "P3" concept is unfortunately not a viable solution as we no longer have trained Flight Engineers, and moving back to 3-crew, even with one jump-seating, could not be practical in the short- or medium-term as "P3"s could not be brought into the industry fast enough.
Although hindsight is, as always "20/20", it seems that we are "hoist by our own petard" having phased out the 3rd cockpit member who, as I recall, was originally a trained engineer who could often fix a snag when away from base by his own skills. Maybe that's no longer feasible with modern aircraft, but it would probably have prevented several events in recent years when one of a pair of pilots have decided to self-destruct and take an entire aircraft's crew and PAX with him.
I'm not convinced that medicos could quickly enough respond to a pilot who, for example, found himself in a emotionally and financially disastrous divorce situation, or a financial catastrophe, and kept it to himself, to avoid this sort of scenario occurring again.
My thoughts (FWIW) - maybe an "Air Marshal" on the jump seat? Or would that be another weak point if it was the Air Marshal that became temporarily unbalanced
Just my 2 cents,