It's not a super common theme but it does exist. The motives could also be related to a dark turn in Harry's character. Maybe in these fanfictions, Harry is influenced by dark magic or has been pushed too far by the Dursleys' constant mistreatment. He might see killing them as the only way to break free from the chains of his past. But this goes against the core values of the original series which promotes forgiveness and love in the face of adversity.
Jealousy could be one motive. They might be jealous of Harry's special status as a wizard. They see him as different and a threat to their 'normal' family life, so they want to get rid of him.
One possible motive could be extreme revenge. After years of being mistreated, locked in a cupboard, and generally being made to feel unwanted, Harry might snap in fanfiction. Another could be a sense of self - preservation if the Dursleys were somehow involved in a plot against Harry's life in the fan - created plot.
One possible motive could be revenge. The Dursleys treated Harry awfully for years, so in fanfiction, he might reach a breaking point. Another could be self - defense if the Dursleys in the fanfiction were to take their abuse to an extreme level.
It's controversial. The Dursleys were Harry's only family (albeit a horrible one) in the Muggle world. Killing them in fanfiction is a very dark take. It's not common because most fanfiction either focuses on the magical adventures, Harry's relationships at Hogwarts, or redeeming the Dursleys rather than such extreme and immoral actions. The original series promotes forgiveness and growth, not revenge - killing.
He could be doing it out of a sense of justice. Despite his family's views, Draco might see that the way the Dursleys treat Harry is wrong and decides to step in.
The Dursleys are a rather uptight and narrow - minded family. In this fanfiction scenario, they could be extremely judgmental of Harry's girlfriend. They might look down on her if she doesn't fit their idea of what a proper person should be like. They may also be secretly afraid that she will expose their mistreatment of Harry, so they could act very defensively during her visit.
One possible motive could be a conflict over their loyalties. Remus is a werewolf and has his own set of insecurities and allegiances. Maybe Snape discovers something about Remus that he threatens to expose, leading Remus to kill him in a moment of panic. For example, if Snape were to find out about Remus endangering students during his werewolf transformations and was about to report him to the authorities.
Perhaps in this fanfiction, Dumbledore has a secret plan related to Harry's power. He might think that by kidnapping Harry, he can train him in isolation to fully develop his magical abilities without the distractions and potential dangers at Hogwarts. It could also be that Dumbledore is trying to hide Harry from Voldemort in a way that no one would suspect, as Voldemort would never think Dumbledore would use such extreme measures against Harry.
One possible storyline could be that the Dursleys' pet, perhaps their cat, discovers Harry's wizarding abilities before the Dursleys do. It might then have some comical or tense interactions with Harry, like trying to stop him from using magic in the house for fear of getting in trouble itself.
One possible plot could be that the Dursleys receive a threat from the wizarding world that they can only be protected from if Harry stays with them and helps. Harry, being a good - hearted person, decides to do so and in the process, he starts to understand them better and grows to love them.