You've hit the nail on the head... but you've sort of whacked your thumb with the hammer. With all of its great ballads, forebitters and drinking songs, the heart of the sea shanty is still its function as a work song -- designed to get people to work together in unison. What good is a common cry of "Haul Away, Joe" when your cargo is being hoisted by an electric winch?
Aside from their musical or other qualities, sea shanties only existed because of that. As for any correllation to the size of the ship, that only applies in modern times inasmuch as the smaller ships don't always have all the necessary gizmos, so men still have to work in unison. Even in the old days, size didn't matter. Ahem. I mean, no shanties were used in the Navy, because any voice but the commander's could interfere with battle. So they achieved work unison by a series of whistles instead of using the songs you and I love.