In the Fan Works section for Light Is Not Good on TV Tropes it says that there are quite a few Kingdom Hearts fics positing that, in order to complete the trifecta of Dark Heartless and Twilight Nobodies, the third faction of evil beings will be light-based and Knight Templar-ish. So my question is, can anyone please give me some story examples that have that premise?

Anything that's a cross over with one of the many, MANY, main Shin Megami Tensei games. The Hosts of Heaven, (any sort of Angle) are very much not your friends in those games. That doesn't mean you should trust the Legions of Hell, either.

Just be warned that a lot of SMT stuff is very dark tone-wise, and tends to deal with less then pleasant topics.

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What about stories that aren't crossovers?

The story the games themselves tell would be good examples. A lot of SMT titles have Older Teen or Mature game ratings. There is a novel adaptation of one of the game series, titled as Quantum Devil Saga: Avatar Tuner.

Just be aware it deals with very dark themes, obligatory cannibalism being one of them.

If you don't want games or novels, an anime called Psycho-Pass might also fall into this category, of law(light) not being as good as it seems.

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I am looking for straight-up Kingdom Hearts fanfics that aren't crossovers in any way, shape and form and nothing else whatsoever. Now then... Do you have any examples?

Ah, I missed the kingdom hearts bit in my sleep deprivation. None off the top of my head. Sorry.