Thrythlind's a) and d) reasons are the main reasons I write fanfic. I used to be horrible at action sequences. I could see them, but the writing of them was not being full of goodities. So I used to sit down and practice writing them. In order to give myself a sense of a complete world, I'd write them in fanfic. I could've just started writing about two people in a fight, another couple in a gunfight, whatever, but they felt hollow without the whole world in place. And since I wanted to focus, I didn't want to worldbuild to get it done. Easiest solution: fanfic.
And of course, there's the fun of it. The Grace & Matt stories, to use my most recent fanfic, are just plain fun. The first one took some plot wrangling, but even that was fun. The hardest thing about the first one was making sure the timelines matched, and the second one doesn't have that problem, exactly. I had fun nudging my style a bit to be more in line with Jim's voice, I had fun inventing characters who'd fit into the world seamlessly, without disrupting the flow of the canon world.
The only other reason I write fanfic is to cover missed opportunities. Every now and then, something I read or watch leaves a huge question mark in my head, and I itch to answer it. Thus, fanfic. Also covered under this is when an author takes a left turn and either does something I despise to the world they created, or just abandons it. Wanting to get back to the world that was, I write fanfic for it until I'm over my mourning period.
Now, all that having been said, lemme get to the question. Is it "better" to play in your own yard or someone else's? That depends on why you're writing what you're writing. If you want to publish, get your own yard. No question. If you just want to write, if you just want to create the stories and maybe post 'em online for ten or twenty people to read, go whichever way the wind blows you. Fanfic can be fun, even if the story you're telling is serious. Original stuff can be fun, too. Feel free to do whatever gives you happy feelings on any particular day.