It should come as no surprise that the 2nd or the third movie would distance itself from the ride that inspired it. The ride itself has been distanced from its own distinctive heritage by making all of its changes. Therefore it is no small wonder that the theme song "yo ho yo ho" was left out of the movie.
IMO the reason the theme or song "Yo Ho a A pirates life for me" was included in the first film is because the first movie was supposed to be able to stand alone not as a sequel but as a single story. The movie was going to be different from but still rely heavily upon the ride in order to appeal to the fan base in order to draw more people to the movie. I do not believe the Disney company anticipated how successful "The Black Pearl" would be, but when they saw it they decided to embrace it (obviously) and allow the movie to take over and supercede in normanative influence the original ride. They did this as a marketing tool both for the upcoming sequels and for the ride and parks themselves that they would cross market each other and hopefully increase interest and profits in both.
"How could they change a hallowed ride in such drastic ways as to allow the movie to inform the ride?" some faithful ask. The POTC ride survived for many years without any change, but the end of its hallowed stature arrived as the culture changed and the people became easily offended and the heads of Disney relented and made the fateful change in the ride to that of men chasing food rather than women.
Yes the original was slightly dated, but it was at the same timeless simply because it was not tied to any modern reference to pop culture. The new changes, however heavily reference the movie which now is incredibly popular, but what will the next 10-20 years bring? Will it seem timeless? No, it will be dated to that blockbuster series from the early years of this millenium. Will it even last so long without further changes? Probably not.
Instead of changing the story line of the ride to reflect the movie they should have refurbished the whole thing and made the same figures they have always had be more animated without messing with the story already present in the ride.
Therefore the reason they no longer have the "yo ho yo ho" song in the second movie and probably won't in the third is because they no longer care for its heritage and soon the traces of what once was will be removed from the ride completely whenever it becomes expedient or economically advantageous to do so. The old song is quaint and too whistful to fit in with the great seriousness with which this movie (and ride) enterprise has taken upon itself in order to garner more money and appeal to the more broad public.
There is more I could say, and and what I have written is probably to some incomplete, but to write more would be to much more than the too much I have already written.
I know this topic (changes to the ride from the movie) has been dealt with in other threads, but I believe it is all part of the same.