I don't see why offline content shouldn't be possible. Especially if it was content that was specifically different from community based online stuff. Like crafting or fishing. these don't require a lot of interaction (although the can!), so there's no reason you couldn't do them off line. But why? Why do these things offline when they can easily be done online. I can't come up with a good reason, and there haven't been any posted here. But that doesn't mean that SE can't find interesting, compelling and fun reasons to make these and other activities available offline. Here's a few ideas:
-Player run shops. You can build, staff and run your own shop. This could be a sim type mini game where players shops ar available in the same way the auction house is now. Walk up to a door in the game, select the player run shop you want to enter and step inside. You can interact with npc shopkeepers, customers and other characters set by the shop owner player. Shop owner players can sell goods they've gathered, as well as goods won through purchasing contracts earned through playing the shop sim. Shop owner players don't have to be in-game to interact with the shop mini game. They can mostly play it, modify it and interact with it without logging into FFXIV. In this case the content isn't really offline, it's just that the mini game shop allows the player to interact without logging in with their character. Extend this idea to player run taverns, restaurants and houses!
-Training. Another mini game that lets characters face off against individual monsters using special equipment of their choosing. This game could serve a few different functions,including letting players test out new items, spells and combat techniques without the risk of death in game. But that's no big deal, right? Maybe the training mini game could also offer victory points to earn special prizes that could be brought into the main game. Cosmetic stuff would be best, I think. This would be a totally offline feature that would still link directly to the online game.
-Library. A special room that can be accessed both in and out of teh game, allowing character to wander through a vast library accessing fictional info about the game world, official info from SE about the game and maybe even a player created and maintained Wiki with game tips and info. This is less of a mini game and more of a virtual library that's accessible both in the game as well as from the quick start menu.
-Earned solo adventures. Rewards for missions/quests/whatever could take the form of fun offline solo missions designed for a single player. These would take place in small, contained areas and would focus on presenting the individual who had earned them with a challenging mini adventure. These could be repeated as often as you wanted, possibly allowing you to earn experience along the way. The benefit here is less about playing offline and more about having an awesome and fun little adventure just for you.
-Pet raising. Chocobo and pet raising would hopefully be part of the main game, but it would be fantastic to be able to monitor and influence my pets development without having to actually log in and run to a stable.
These are just ideas. There's a lot SE can do with out of game content.