re: Why are ship captains still expected to go down with ship

here's a good summary from reddit/r/askhistorians

The role of the Captain is to the "Merchant Marine Officers Handbook" is to ensure the safety and wellbeing of his passengers or crew, the idea that the captain must go down with the ship is slightly untrue. He must ensure that every one else is safely evacuated first before leaving himself. In the US navy and coast guard there is a similar order, saying that the Captain must be the last one to leave.

I am relying on a source written by an American so unfortunately I can't say much for certain but I would imagine this applies to other navies around the world, as evacuating a ship with a thousand plus people on it requires a great deal of organisation, thusly requiring the captain's presence.

The stigma is with not ensuring that your crew and passengers are properly taken care of first rather than with not dying with the ship.This source has some really good stories of captains praised for their efforts who survived

LINK

As for where it came from it doesn't really go too far back in history, I mean I am not an expert in martime history but given that the vast majority of sailors could not swim boats were not equipped nor trained for evacuation. By the time it came to abandoning ship most were resigned to their fates and the tales that followed were more of a romantic reimagination of the terrors of naval warfare than an actual law.