Well, it's hard to say it's a widely popular genre on its own. The Naruto fandom has a vast range of fanfic types. While the idea of Naruto being a cold and distant shinobi might attract some readers who like exploring different character portrayals, it's not as mainstream as some other common themes like Naruto achieving new powerful jutsus or his relationships with other main characters. There are so many different takes on Naruto in fanfics, and this rather 'edgy' or different view might only appeal to a niche group within the large Naruto fan base.
His relationship with Sakura would definitely be affected. Sakura, who has always known the warm - hearted Naruto, would be shocked and confused. She might try to reach out to him at first, but if he keeps pushing her away, she could become frustrated or even give up. Their friendship would be strained.
One possible reason could be a major betrayal. Maybe someone he trusted deeply, like a close friend or a mentor, turned against him. This would make him lose faith in people and become cold as a form of self - protection.
Another reason could be the influence of a powerful and dark entity. If Naruto is somehow possessed or influenced by a dark chakra or a malevolent spirit, it might change his personality completely. He could start to push away people who care about him because the entity wants him to isolate himself and be more vulnerable to its control.
One reason could be to explore a different side of Naruto's character. In the original series, he's so warm - hearted, but by making him cold and distant, the writer can show how different events could have shaped him in an alternate way. Maybe he faced more hardships or betrayals that led to this change.
One possible plot could be that Naruto has faced so many betrayals. Maybe his friends turn on him due to some false accusations. This shatters his warm - hearted nature, and he becomes cold as a defense mechanism. He starts to isolate himself and no longer trusts easily.
The author could show his coldness through his limited dialogue. For example, Harry might give short, curt responses to others. This would immediately signal his distance.
One possibility is that Naruto might feel a sense of isolation. Since Sasuke has achieved the highest position in the village, Naruto might feel like his own journey and achievements are overshadowed. He could become cold as he withdraws into himself, thinking that he no longer has a clear purpose in the village where his best friend now holds all the power.
If Naruto becomes cold, his relationship with Hinata would be severely affected. Hinata, who loves him for his warm heart, might be at a loss. Naruto might start to push her away, not allowing her to get close. His friends from Team 7 might try to bring back the old Naruto, but his coldness would create a rift between them.