Consent, for me, is the heart of this issue. If a writer wants to allow or even encourage others to use their worlds and characters, that's fine. Their call. If a writer would prefer not to allow that... well, I think their wishes should be respected.
Myself, I think the writers who allow fan fiction are making a mistake. I am not saying here that the people who write fan fiction are evil or immoral or untrustworthy. The vast majority of them are honest and sincere and passionate about whatever work they chose to base their fictions on, and have only the best of intentions for the original author. But (1) there are always a few, in any group, who are perhaps less wonderful, and (2) this door, once opened, can be very difficult to close again.
Most of us laboring in the genres of science fiction and fantasy (but perhaps not Diana Gabaldon, who comes from outside SF and thus may not be familiar with the case I am about to cite) had a lesson in the dangers of permitting fan fiction a couple of decades back, courtesy of Marion Zimmer Bradley. MZB had been an author who not only allowed fan fiction based on her Darkover series, but actively encouraged it... even read and critiqued the stories of her fans. All was happiness and joy, until one day she encountered in one such fan story an idea similar to one she was using in her current Darkover novel-in-progress. MZB wrote to the fan, explained the situation, even offered a token payment and an acknowledgement in the book. The fan replied that she wanted full co-authorship of said book, and half the money, or she would sue. MZB scrapped the novel instead, rather than risk a lawsuit. She also stopped encouraging and reading fan fiction, and wrote an account of this incident for the SFWA FORUM to warn other writers of the potential pitfalls of same.
That was twenty years ago or thereabouts, but that episode had a profound effect on me and, I suspect, on many other SF and fantasy writers of my generation.GRRM's article was in response to a post on the same topic by Diana Gabaldon, which caused a bit of a shitstorm.
It was quite interesting to read what people think does and doesn't constitute fanfic, and their various explanations/excuses for why they write/read it. It's such a complicated issue that even GRRM has subsequently admitted he's not totally clued-up on the legalities of it all.
My own feelings towards fanfic are pretty straightforward: I think it's pointless.
If you want to be a writer, write your own material. A lot of people have argued they write fanfic to develop their writing ability, but I think you'll improve much more quickly and to a greater extent if you're creating your own characters. After all, characters are the heart of every story, and pissing about with characters that someone else has devised and developed isn't going to help you develop a strong grasp of characterization. And yeah, perhaps by writing fanfic you can develop your skills in other aspects of writing - but you can do so equally well by writing your own original material.
As for the reading side of things, I just don't get it. I don't have enough time to read all the 'proper' books I've got sitting on my living room table, let alone time to trawl through countless poorly-written, ill-conceived fanfic. Furthermore, fanfic isn't canon - so what's the point? You're reading stories about events that - as far as the original creator of the world/characters is concerned - never happened. So why bother? I just can't see the sense of it.
No matter what angle I look at it, 'serious' fanfic just appears to me to be masturbation in prose form.