I haven't actually come across a 'Dursleys kills Harry Potter' fanfiction. It's a rather disturbing concept considering how the story of Harry Potter is centered around his survival against Voldemort. The Dursleys are just part of his Muggle upbringing with their own brand of meanness. If there were such a fanfiction, it would probably change the whole trajectory of the story. For example, the wizarding world would lose its Boy Who Lived, and it would be interesting to see how the characters like Dumbledore or Hermione would react to such a tragic event.
There are likely 'Harry Potter Kills Dursleys' fanfictions. Fanfic writers often like to explore extreme scenarios. In this case, it could be a way to show how far Harry could be pushed. It might also be a commentary on the Dursleys' horrible treatment of Harry. But this goes against the somewhat forgiving nature of Harry in the original books.
Some authors might create it as an exercise in 'what - if' scenarios. They want to break the established narrative and see how different characters would react if Harry was killed so early. Also, it could be a way to explore the Dursleys' characters more deeply, showing just how far their hatred for Harry could go.
In some interpretations, it could be that Harry finally snaps after years of abuse from the Dursleys. Maybe they pushed him too far one day and in a fit of rage, he uses his magic to end their lives. It's a very dark and extreme take on the Harry Potter universe.
The original Harry Potter series promotes forgiveness and the power of love. Harry is shown to be a kind - hearted character who believes in the good in people. But in the 'harry kills the dursleys fanfiction', it goes against this. It shows a more vengeful and darker side of Harry that is not in line with his character in the books. It also changes the family dynamic aspect which is an important part of the original story.
It would completely shatter the positive perception of Harry. He is known for his kindness and ability to forgive. Such an act would make him seem like a cold - blooded killer, which is the opposite of how he is in the original series.
It could start with a build - up of small incidents. For example, the Dursleys constantly belittling him even after he has proven himself in the wizarding world. Then, one major event, like the Dursleys trying to sell his magic items or preventing him from going back to Hogwarts, causes Harry to snap. His killing of the Dursleys could then lead to a search for redemption or a fight against those who want to punish him unjustly, as he was pushed to his limits by their cruelty.
One way the Dursleys can be good in fanfiction is if they are forced to face the consequences of their actions early on. For instance, they might receive a warning from the wizarding world that if they don't treat Harry well, there will be serious repercussions. So they start to be nicer to him. They could provide him with a proper room, better food, and allow him to have friends over.
In some Harry Potter fanfictions, the Dursleys are depicted as nice. This could be a really interesting take. It might show how they could have been different if they hadn't been so influenced by their dislike for magic. Maybe they could have supported Harry more, or at least been less cruel. For example, a fanfiction could explore a scenario where Vernon Dursleys actually encourages Harry's academic achievements at school, instead of always putting him down.