One reason could be for guidance. Naruto often looks up to Kakashi and might need his advice on a difficult situation, like dealing with a new powerful enemy.
Yes, there are some. However, the popularity can vary. Some are popular within certain fan communities. You can usually find them on fanfiction - specific websites by using relevant search terms like 'Naruto modeled after Kakashi' or something similar.
In this fanfiction, Naruto might be on a mission to find Kakashi for some crucial training. Maybe he wants to learn a new jutsu that only Kakashi can teach him.
A 'Naruto modeled after Kakashi' fanfiction could see Naruto with a changed appearance to some extent. He might start wearing his headband in a similar way to Kakashi, or even have a similar style of clothing. In terms of his ninja skills, he could master the Sharingan - like abilities in some form, perhaps a new jutsu inspired by it. His mentoring style could also change, becoming more like Kakashi's, being tough but fair with his students or comrades.
Naruto is known for his never - give - up attitude. Young Kakashi, who has faced a lot of hardships in his life, has a somewhat jaded view. Their personalities would interact in an interesting way. Naruto might try to show Kakashi that there is always hope, while Kakashi could teach Naruto about the harsh realities of the ninja world. This exchange could lead to both of them growing as characters.
Well, one similarity could be their determination. In the fanfic, like in the original series, both Naruto and Kakashi are very determined. Naruto is always striving to become Hokage and Kakashi has his own goals and missions he's dedicated to. They also might share similar combat styles in the fanfic, perhaps Naruto starts to adopt some of Kakashi's strategic thinking during battles.
His ninja skills would probably develop in a different way. Without Kakashi's guidance, he'd have to figure things out on his own. This might lead to some unorthodox training methods and a unique fighting style. For example, he might focus more on his natural instincts and less on the traditional teachings he received from Kakashi. He could also form new alliances with characters who are also outsiders or misfits in the ninja world, creating a new support system for himself.
Sasuke could be a popular character. He might be involved in the story in a way that either helps or hinders the situation where Naruto hurts Kakashi. For example, if Sasuke tries to stop Naruto from doing something stupid that would hurt Kakashi.
Another reason could be related to Kakashi's past actions. If there are some secrets or things Kakashi did in the past that come to light and Naruto doesn't like them, he could snap at Kakashi. Naruto has a strong sense of justice and loyalty, so if he feels betrayed or misled by Kakashi, his reaction could be to snap.
Well, it could be about Kakashi finally finding Obito after a long search. Maybe Obito has changed a great deal, and Kakashi has to come to terms with this new version of his old friend. They might have a battle first due to their different paths, but then they start to talk and remember their past together, like their time as teammates in Team Minato.