Maybe it's because Gaara sees a lot of himself in Naruto. They both had difficult pasts and were kind of loners at first. Gaara wants to protect Naruto from the pain he once endured.
One possible scenario in this fanfiction could be that Naruto's sister constantly interferes in his ninja training. She might think the training is too dangerous for him and tries to stop him from taking on challenging missions. For example, when Naruto is about to go on a mission to the Land of Waves, his sister could try to convince the Hokage not to send him, believing that he's not ready yet. This would add a whole new layer of conflict to the story, not just between Naruto and his sister, but also with the village's expectations of Naruto as a ninja.
One aspect of a 'Naruto: Overprotective Kushina' fanfiction could be exploring Kushina's overprotectiveness in Naruto's early life. Maybe she's constantly hovering, fearing for his safety due to her own past traumas. This could lead to some interesting character dynamics, like Naruto feeling smothered at times but also understanding her love.
Well, in the fanfiction world, Minato might be overprotective of fem Naruto because he lost her once. Maybe there was some kind of incident in the past where Naruto was in great danger or even 'died' briefly. This made Minato extremely paranoid about losing her again, so he goes overboard with the protection. He might also be influenced by the fact that as a female in their world, Naruto could face different and perhaps more complex challenges than if she were male, like discrimination or special treatment from certain groups.
The plot could revolve around Kushina trying to keep Naruto away from any potential harm. For example, she might not allow him to go on certain missions or even just play in dangerous areas. This would create a conflict as Naruto has his own desires to prove himself and be a normal ninja.
In the Naruto universe, Naruto is a powerful character. Hinata, while strong in her own right, is not as physically dominant as Naruto in many fan interpretations. Naruto's overprotectiveness can show his growth as a character who now has someone he cares deeply about. It also creates drama and tension. For example, when they face enemies together, Naruto's overprotective nature can lead to him making rash decisions or Hinata trying to prove herself despite his protection, which makes for an interesting plot in fanfiction.
There are quite a few out there. In a lot of these 'Naruto overprotective sister fanfiction' stories, the sister is usually a new character created by the author. Her overprotective behavior can stem from Naruto's status as a jinchuriki or simply because she loves him dearly. For instance, she might train secretly to be strong enough to protect him. These fanfictions can offer a different perspective on Naruto's growth and the relationships he forms within the Naruto universe.
It's appealing because it adds a new family - related angle. Naruto didn't really have a strong family presence in the original, so having an overprotective sister fills that gap.
One popular 'Naruto overprotective mother fanfiction' might be 'A Mother's Love'. In this, Naruto's mother, Kushina, is brought back somehow and she becomes extremely overprotective. She doesn't let Naruto go on any dangerous missions without her supervision. Another could be 'Overprotective Momma Uzumaki' where she fusses over Naruto's every move, from his training to his friendships, making for some really heart - warming and humorous situations.
Well, often in Naruto overprotective family fanfiction, a major theme is the family's struggle to balance their overprotectiveness with Naruto's need for independence. They love him so much that they don't want him to get hurt, but at the same time, Naruto is a growing shinobi who needs to face challenges. Also, there can be themes of family secrets. The family might keep things from Naruto to protect him, which then leads to misunderstandings and plot twists.