The following was told to me by Royal Caribbean, but I have to think it holds true for Carnival too. At least to some extent.
The production shows cost several million dollars to develop and produce. Productions will start on sound stages the cruise line has in Florida, and will typically take a year to 18 months before being ready to move aboard the ships.
Obtaining and paying for rights to songs, themes, even costumes, adds up. I'll bet you didn't think a costume might be covered by trademark. And everyone is well aware of copyrights and royalties for songs, show themes, and character names.
So once a major cruise line gets a show ready for prime time they will use it for at least 3 years and sometimes longer.
If they bought the rights to use songs from All That Jazz for 5 years, they are going to use them for every one of those 5 years. They do move shows through the fleet, with new productions going to the newest ships and the other shows cascading down to the oldest ships and then being retired. Some shows, because of the need for special stages and equipment, will remain on the same ships.