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Love it! Even the horrible stuff has merits. Soon those squealing twleve-year-olds who don't know how to work a spellcheck or a penis will evolve into great writers, or at least decent writers.
True, people should strive for writing they can publish, but many books, comics, and movies have elements of fanfiction about them, so it's not so much 'write your own stuff' as it is 'work what you love to write into something you can publish.' At least, that's how I see it, because I want to be a published author.
A lot of people seem perfectly content to just write fanfic and squee with their friends about whatever show/book/comic/movie and that's all. It's a fun thing for them to do, a safe place for them to relax and hang out online. It's a lot of that for me too, with some sense of 'this is practice' thrown in.
I think authors who forbid fanfiction of their work are unaware of how fanfic can increase a fanbase, make casual fans into hardcore ones, and improve the writing skills of struggling teenagers. I think it's rude and stupid to forbid an entire aspect of a fanbase. Are they allowed to make icons, fanart, fanmixes, of the fanfic-forbidden work? Are they allowed to discuss it online? Are they allowed to dress up as their favorite characters? It's not as though they can publish their fanfic, so why pitch a fit?