I play because those ores won't mine themselves!
Seriously though, I do love a good grind. I get intrinsic value out of it, rather than just extrinsic.

In my case, I do not get much time to play between working full time, Studying for my degree, doing house work, pursuing other hobbies, and being part of my family. So I have a constant backlog of stuff to do, and lots of story that I have still not yet experienced.
Also, since getting a house I have discovered the world of crafting furniture and making gils and decorating - and that novelty is a long way from wearing off (especially as I can upgrade in size when I save up enough which will then give me even more to do)