I wrote fanfiction very successfully for a number of years. By successfully (which I can't seem to spell properly this morning) what I mean is, I was able to write a series of stories, one every week or so, and maintain a steady audience that kept coming back.
(if you're not familiar with fanfiction: one of the big fads, back when I did it, was to create your own "series" with seasons, a certain number of episodes, everything. Not just one off stories, but actual series. I did it for three years.)
I learned how to maintain a body of characters. I learned how to appeal to readers. I learned how to tell a story, beginning, middle, and end. I learned how to extend a story for several episodes without it becoming dull (something which eventually filtered into my novel writing).
I learned a lot from fanfiction. When I started, I was just cutting my teeth writing. When I finished, I was able to tell good stories about people you would care about. Some of what I'd written doesn't hold up so well, but a lot of it still reads comfortably and tells an interesting story.
I have no problem with fanfiction. Or at least, the fanfiction of the period when I was doing it. I'm loathe to use the word "generation," but the next generation of fanfiction seems to have gone for self gratification and bad writing more than anything else. Most of us who were involved then wrote to get better, wrote to entertain, and most of all, wrote as much as we damn well could.
These days, I see a lot of self-indulgent tripe. I suppose there was always probably a fair bit of that. Now, it's just dominant.
...
One of the biggest arguments against fanfiction (or, sometimes condescendingly made for fanfiction) is, "You're not creating your own characters or universe, right? So it's easier. You're just playing with someone else's toys, instead of your own."
Again, I created all my own characters, all my own stories, all my own problems and resolutions and settings and everything. I was playing in someone else's sandbox (Star Trek) but short of occasionally making references to show you where I was in the continuity, the series I wrote. My stories were my own.