In my opinion, there are many different factors to these "distinct" LBT stories in any fanfiction. Most of the stuff in the fics you mentioned are by people who writes them depending on the mood they're in or in the style those people desire. Some of the stories containing sexuality, violence, or any other not-for-children material are by those would write any fanfiction in that method, since I have seen Pokemon, Digimon, and Disney stories written that way (I fell into a few websites that were too much for my tender virgin eyes
(Seriously, I went into them on accident)).
It is really hard nowadays to find someone who writes fanfictions of something they really like. The only story I read so far in fanfiction.net that has a strong grasp to LBT was "The Big Quarrel" by you, Malte. I haven't read ALL the LBT stories, but yours is number one in my book
.