Air sound, thanks for taking the time to reply. I do appreciate that but I still question either your qualification to comment on this or your research (or even both).
I am an airline pilot of 20 years and am in management. I have participated in creating the safety case and have had comms with airline management of most of the bigger UK airlines. I can categorically say that most if not all of them do not show that "On balance, an extra crew member on the flight deck is probably beneficial".
PR with this issue is the problem and what the public perceive to be "safer" policies but which actually aren't. So your comments do not help safety they just add credibility to incorrect public perception that makes it harder to move back to the better policy of NOT having a 2 person flight deck policy.
I am not at liberty to reveal my company's safety case nor am I at liberty to speak to the press, either anonymously or not, as what is said to the press is a corporate decision made above my pay level.
I would suggest that you try to use your contacts to have a look at these safety cases, if you are unable to gain access then your research is incomplete and so your comments are based on incorrect assumptions.