People will argue until they're blue in the face that you MUST get a passport, even on a closed loop cruise because "in case of emergency" do you want to spend time in the embassy working out paperwork? It's an "insurance policy".
So what in goodness gracious is the logic behind leaving it on the ship? Say you're on an excursion and you are in a car wreck. Transported to emergency room with a broken leg and miss the ship. If your passport is on the ship then you'll have to *spend time in the embassy working out paperwork*! WHAT??
What is the advantage of having a passport? For closed loop, the *only* benefit of a passport is to avoid embassy/state department hassle in the case you'll need to fly home. If you don't have it on you .. it seems to me anyhow.. that all benefit of having it is gone.
Plus, let's be realistic. What is the big deal if it is stolen? I mean, it stinks, you don't want that to happen -- but you report it and move on right? I suppose re-entry to the US would be a problem -- but that will be a hassle if *any* of my ID is stolen. Why would DCL suggest you leave the passport on the ship?