One possible fanfiction could be about Kakashi getting injured during a mission. Maybe he's protecting his team and takes a powerful jutsu head - on. His students then have to figure out how to get him to safety and find a way to heal him. It could show their growth as they face this difficult situation.
One reason could be that he sees Naruto as a younger version of himself in some ways. Both have had their share of loneliness and challenges growing up. Kakashi may want to prevent Naruto from going through the same pain he did. Another reason is Naruto's importance to the village. As the jinchuriki of the Nine - Tails, Naruto is a key asset. Kakashi, being a loyal ninja, wants to protect the village's future which is tied to Naruto.
One possible scenario in such a fanfiction could be that Kakashi, while in ANBU, is assigned to protect Kushina during her pregnancy. He might have to deal with various threats against her and the unborn child. This could lead to some intense action scenes and also some character - development moments for Kakashi as he realizes the importance of protecting new life.
One reason is Naruto's vast chakra reserve. His Uzumaki heritage gives him an almost unlimited supply, which can be emphasized more in fanfic. So he can keep going in a fight longer than Kakashi.
Yes, there might be some out there. Fanfiction often explores creative and non - canonical relationships. However, it's a rather unique concept as in the original Naruto series, Kakashi, Rin and Sakura have different storylines. Kakashi was Sakura's teacher, and Rin was Kakashi's teammate from his early days. This kind of fanfiction would take a lot of creative liberty to build a believable backstory and connection between them.
Well, perhaps in the fanfiction, there's a mission where they are the only survivors and during their time of isolation, they develop a deep bond which leads to Sakura getting pregnant. The story could then revolve around how they deal with this new situation, with Kakashi trying to protect Sakura and the unborn child from any potential threats.
I'm not sure about specific fanfictions on this. You could try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own. Just type in 'Kakashi and Kurenai pregnant' in their search bars and see what comes up.
One great fanfiction is 'Kakashi's Unwavering Shield'. In this story, Kakashi goes to extreme lengths to protect Naruto from various threats within the village. He even stands up against the council when they try to make unfair decisions regarding Naruto. It really shows the depth of his protectiveness.
One great Kakashi hurt fanfiction could be 'Kakashi's Trial'. In this story, Kakashi is hurt during a difficult mission. The author vividly describes his physical pain and the emotional turmoil he goes through. His friends in the story rally around him, which shows their deep bond. It also delves into how Kakashi copes with his injury and the fear of not being able to return to his full strength as a ninja.
One possible plotline could be Naruto growing up with Kakashi's unique training methods. Since Kakashi is known for his strict and strategic training, Naruto might become an even more formidable ninja at a younger age. He could inherit Kakashi's Sharingan abilities in some creative way in this fanfiction world, which would give him a whole new set of skills to master.