I like fanfiction, because in its own way, it’s a little bit like literary analysis. It’s showing instead of telling. You could write an essay on the sexual tension between Kirk and Spock, or you could pair them up in a fic.
In some schools of literary analysis, we’re taught that “the author is dead.” Meaning, the authors intentions don’t matter. Whether they liked this character, or hated that plot twist, or meant for the rain to symbolize sadness, is completely irrelevant. The work speaks for itself, and we’re only interested in what it has to say.
This is why I don’t particularly care that JK Rowling said she regretted pairing up Ron and Hermione. I’m mean, it’s interesting; I find her views on the story, and her experiences writing it, really fascinating. But it doesn’t change anything, and fans don’t need to feel conflicted or validated by her statement. It was also really interesting when she told us Dumbledore was gay, but it didn’t really affect the story. It didn’t add subtext that wasn’t already there, or validate any arguments. Authors decide how to write their books, yes, but once they’re published, they can’t change anything (unless they write more, of course). That’s the exciting/terrifying thing about writing. It’s permanent.
Fanfiction, on the other hand, can do anything. It can take the smallest interaction between characters, and turn it into a shipping war. It can take the merest hints, and create new and unexpected plot-twists. It can highlight things everyone else overlooked. And unlike books, its not permanent. You can change the rules in each fic; you can retroactively de-canonize moments in the original story; you can kill off or bring back beloved characters. Although each fic creates it’s own canon, fanfic writers can always start a new fic, and re-imagine the world all over again. And with a few clicks of your mouse, you can remove the story entirely, leaving it only in the minds of your readers.
There’s a freedom to fanfiction, because it’s unofficial, because it can be written by anyone. It can be full of literary insight, or just basic wish-fulfillment. The only rules are, be entertaining; have fun; try to write the characters as true as you can.
Lucy in Bookland 
As a creator of fanworks, I do consider what I do with the characters permanent within my own small sub universe. For example,if a character has a child, that child has to appear in subsequent stories. Of course, someone else could borrow from my story as well as the original and change everything, but once published I consider the events in the story permanent within that universe.
Definitely! Each fanfiction writer constructs their own direction for the world, which can be as consistent within itself as that author chooses. However, the original work is not changed by these creations (unless you get into headcanons, which is another discussion all together). That author is also not tied solely to that version. They can write fanfiction in the same fandom, but without tying it in to their other stories, so there’s always a chance to go explore different possibilities. Say you write a long-standing Star Trek fic, which has a lot of new characters, new character development, new pairings. You can still publish a separate story (or stories) which branch off Star Trek but have nothing to do with your other fic’s universe. This is a freedom that exists in fanfiction, which is harder to obtain for a novelist. It’s not so much that published books are permanent and fanfiction isn’t, it’s that fanfiction gives an opportunity for something permanent to still grow.
I’ve tried to clarify this a bit more in the original post. Thanks for pointing it out!