There are many reasons given for why passengers and crew of airlines and ships are referred to collectively as “souls on board.”
But one that’s not mentioned is the fact that the 19th century age of the steamship, when the practice seems to have originated, was much more religious than now.
People believed in souls then as they pretty much do not now. At least not officially or in the news media. So it was likely more than convenience sake in radio procedure to refer to passengers and crew as souls on board.