Who cares? Or really listens?
When I was working my balls off in low cost world as a Captain (only ever an FO before in full service/charter), I always gave the FO's I flew with free rein to make the "welcome on board" PA.
3 reasons for this:
1) I was generally busy signing various bits of paper. LMC's etc;
2) The FO had a mouth, a licence and a good idea of what he/she/we were doing (caveat:if there was weather/delay/tech etc. I'd do it): therefore I always felt they were qualified to welcome passengers on board on my behalf, and;
3) My PA's were never that good anyway.
CRM points us to a 2 crew operation. I cannot stand hearing "MY First Officer" or when a Captain completely fails to introduce the other pilot in the flightdeck (and it COULD be another Captain) in a welcome onboard speech.
Why shouldn't an FO make the speech? It's not as if we are in the flying boat era anymore.