The whole
PR business of should or should not the F/O or S/O be mentioned is a case of the
PR horse being put too far in front of the cart.
Whilst surveys may well indicate that pax prefer to believe that the Captain is actually flying, because they believe the Captain to be the more experienced pilot on board, I don't believe there exists the potential passenger, who will decide whether to fly, or which airline to fly on, based on who is perceived to be flying, or who makes the P.A.
What would have
far more impact from a
PR point of view, is happy and pleasant service from cabin crew. As close to on time operations from the whole airline, and a confident sounding P.A. from whom ever makes it.
Some P.A.s I've heard over the years would put the frighteners on any one!