I bought a Casio atomic watch that I have to point toward Colorado so it updates every morning. It is sort of a pain to manually set it. Lousy directions and controls. It has an international function so I can have one time zone on the analog display and another one on the small LCD screen. It is my knock-around watch for those non-Rolex moments, although the Casio is obviously more accurate.
I can see both sides of the argument for the ships staying on homeport time or changing with the local time zones. In the latter, if someone is in a bar on Cozumel and the clock says 3pm they know the ship is also at 3pm. Either way, there are always people who don't pay attention to the announcements or read the daily schedule.