The flaw theory is interesting, but I have a different view. I don't think it's flaws per se that attract fans, but gaps in the story. Aspects of plot or character or milieu or ideas that aren't completely fleshed out.
Most fanfic by far (in my experience) is written about media properties; there's considerably less fanfic for written works. No matter how good the writing, 42-44 minutes of story per episode requires that they cut away anything that doesn't directly add to the story they're telling; so a lot of good material never gets aired even if it was written or even filmed. That leaves a lot of room for fans to explore themes and ideas that were barely touched upon or only implied--though that ties in with the "unfinished quality" you mention.
Also, fanfic affords an opportunity to do things with the characters that will never, ever* happen in canon. Character deaths, disasters, post-apocalyptic situations, variant milieus, and--my personal favorite, I should confess, and what I got into fanfic for--crossover tales with other fandoms.
*yes, yes, there are many exceptions. but as a rule, the producers aren't going to kill off their heroes or even make major changes to their lives for at least most of the run of a show. No so fanfic.
no subject
Most fanfic by far (in my experience) is written about media properties; there's considerably less fanfic for written works. No matter how good the writing, 42-44 minutes of story per episode requires that they cut away anything that doesn't directly add to the story they're telling; so a lot of good material never gets aired even if it was written or even filmed. That leaves a lot of room for fans to explore themes and ideas that were barely touched upon or only implied--though that ties in with the "unfinished quality" you mention.
Also, fanfic affords an opportunity to do things with the characters that will never, ever* happen in canon. Character deaths, disasters, post-apocalyptic situations, variant milieus, and--my personal favorite, I should confess, and what I got into fanfic for--crossover tales with other fandoms.
*yes, yes, there are many exceptions. but as a rule, the producers aren't going to kill off their heroes or even make major changes to their lives for at least most of the run of a show. No so fanfic.