So the agreements say a nation who signed on to these agreements must treat another signed nation’s military personnel a certain way and civilian non-combatants another way. Think of WWII in Europe. Breaking these agreements is a war crime.
Those agreements don’t say how to treat illegal combatants such as ISIL, al Queda, or American civilian mariners who launch rockets at another signed nation.
The chain-of-command isn’t to mitigate confusion or increase efficiency. It’s to provide legal protections to the military and civilians on board.
There are some civilians on USN ships but these tend to be few. What has been proposed here and there is replacing some USN with civilians in jobs like specialized technology.
I recall a few years back some talk about putting civilian engineers on warships. The idea was that civilians would be better trained and more experienced (and cost less). They wouldn’t promote out, and wouldn’t have sea-shore rotations where their skills would atrophy. This could mitigate some of the problems the newer ships are having.
Think how much we pay an enlisted sailor to cook. A culinary specialist spends most of his or her career attached to shore. After twenty years we pay retirement for life. Plus the GI bill, medical, their family, relocation and housing to name a few. What if we replaced culinary specialists with civilians? The cost savings would be big.
Anyhow, I hope you get the idea. Turning a whole ship over to civilians except for the war fighting parts would save a fortune.