With the caveat that it was a while ago....
.....the RAF deemed "captaincy" indivisible. As an ex-kipper fleet back-end captain I always accepted that if P1 ran off the concrete that I would be there facing the music beside him.
The USN in their MPA fleet DID divide the responsibility so the LHS pilot was responsible for the safety of the a/c,crew, and the "Mission Commander" was usually the tactical coordinator (TACCO) and was responsible for the proper execution of the briefed mission.
The USAF as far as I found it was always the P1 who was the captain.
As an illustration I remember being briefed very sternly by a major on an NAEW that HE was the captain and that what HE said WENT. I went up to the flight deck at one point and asked him what exactly HIS crew was doing, Holding over Aalborg in a race track was the reply. But what are THE CREW doing after all YOU'RE in charge.
"Aft of the flight deck door is mission crew **** let them get on with it." Didn't know and didn't care
"aye that'll be right" as they say in Glasgow.
I was fortunate with my P1 who never ever put me in an invidious position but after I left and he became captain he put himself in a VERY invidious position.
As in all things communication is the key to making things like this work. It isn't always easy. Later it became CRM, but the essentials are the same.
The Ancient Mariner