Well, it could be due to a build-up of frustration and a sense of hopelessness in trying to reform the Joker. Also, maybe in that particular comic's storyline, the circumstances are extreme and Batman makes a desperate choice.
The Joker is such an iconic and unpredictable character. Knowing his origin might limit the sense of dread and randomness he embodies. His lack of a defined origin makes him a symbol of pure chaos that can strike at any time, in any way, without the need for a backstory to justify his actions.
Batman typically refrains from killing the Joker in the comics. This is because Batman believes in justice, not vengeance, and killing would go against his principles. Also, keeping the Joker alive creates ongoing story arcs and challenges for Batman to overcome through non-lethal means.
It can completely change it. Usually, there's this cat - and - mouse game between them. But when Batman hurts the Joker in fanfiction, it might make the Joker more vengeful. He could become even more obsessed with getting back at Batman.
Because the mystery around the Joker is part of what makes him so fascinating. His chaotic nature is better left un - explained by a traditional origin story.
Well, Batman brings a unique set of skills. He's a brilliant detective. In fanfiction, his detective skills can be used to solve complex mysteries that the Justice League might face. For example, when dealing with a villain who leaves no obvious clues, Batman can analyze the situation and find the hidden patterns. Also, his strategic mind is crucial. He can plan out battle strategies that the Justice League can follow to defeat powerful enemies.