The interesting thing about Moogles in Final Fantasy XIV is that they are only found in The Black Shroud. They are rare and not common anymore due to trappers capturing them and selling them on Black Markets for some reason or another.

You learn a lot about this from the Lancer Class Quests in the game. Unfortunately, the way the writers have wirtten them into the story makes it kind of tricky to incorporate them in more activities such as a "Moogle Mail Service" or a helper for your "Mog House" and such.

In this game they are more like protectors hiding in the woods and emerging when you are about to potentially harm an elemental or other sacred offering from the forest. Also, it's rather unfortunate, because that means the ONLY time you can even interact with a Moogle is during a Main/Class Quest, and those only come once per character, for the time being.

I would love to see some side quests or additions to the story that would go in more depth with the lack of Moogles and where they all went. Because from what I've seen so far, they don't seem to be registered very well in delivering mail to all of Eorzeans or anything like that, which is a shame. They seem more written as hidden protector of the Twelveswood and the sorts, appearing only when danger strikes and also unable to leave the forest unharmed.

At least, that's what I've collected from my experiences with them, so far.