I don't think the analogy fits.
Everyone knew that most of the people on the sinking Titanic were going to die, especially that the crew and captain were going to die. So there was nothing to be gained by changing the captain to see how he and the rest of the crew would perform, for the purposes of future evaluations. Saving as many as lives as possible was the only thing that mattered.
During a teams losing season, no one is going to die, so you have future decisions to make about who to keep and who to move on from. In a lost season, evaluating players and coaches is one of the few productive things you can do and it's an important thing to do.