I agree and you touched on some of them already. Here are some of my thoughts:

One app that has about 2 to 3 things you can do in that mobile device (default).

1. Auction House - buy things using either gil or real money
2. House Maintenance - this too can be connected to the auction house, using multitouch functionality to move stuff around in 3D environment
3. Crafting - you can do this in your house and have access to auction house.

Other apps that can be added

4. 3D Maps (google map style with street view) - that you already discovered in game or you can purchase. These wont just be mere apps, these maps you can move around using multitouch set markers, zoom in closer to see whats in that area, mobs, possible NM, HNM, chest and the levels safe to go there. etc. All of this is connected to you main account.

5. Character design and creation - this will be an app that has your current character and you can use the auction house app to buy things for it which can then be reflected in the actual game.

6. In order to make this a must get and to make the apps more attractive there should be exclusive items from FFXIV mobile. That includes items, armor, weapons, furniture, maps etc.

wow this triggered so many ideas ! I even have ideas on how this should look like from a UI stand point!

I'll post more later!