It could potentially improve their relationship. Since Naruto is not involved with Sakura, there's no love triangle tension between them regarding Sakura. This might allow Naruto and Sasuke to focus more on their own friendship and mutual respect.
One idea could be a story where Sasuke and Naruto have to team up again for a dangerous mission, and Hinata and Sakura also join in. During the mission, Hinata might use her Byakugan to detect hidden enemies, while Sakura uses her medical and combat skills to support the team. And Sasuke and Naruto could have some deep conversations about their past and future, like they did in the original series.
One great 'Naruto Hinata Sasuke Sakura' fanfiction is 'The Bonds Beyond'. It focuses on how their relationships evolve in a post - war Konoha. The story does a wonderful job of exploring the unspoken feelings between Hinata and Naruto, as well as Sakura's growth as a medic - ninja while still having complex interactions with Sasuke. Another interesting one is 'Team 7's New Beginnings' which takes a fresh look at how they work together on new missions, with some unexpected twists in their character dynamics.
One great fanfiction could be one where Sasuke and Sakura go on a mission together after the main events in the series. They face a new threat and during this, their relationship deepens in a way that shows their growth from the original story. Another could be a Naruto and Hinata story where they are on a diplomatic mission to another village and have to deal with cultural differences. There are also some fanfictions that focus on all four characters training together in a new kind of ninja art that combines their unique skills.
One possible reason could be Hinata's unwavering loyalty. Throughout the series, Hinata has always been there for Naruto, believing in him even when others didn't. In contrast, Sakura was often more focused on Sasuke. So Naruto might see Hinata as someone who truly understands and supports him.
A good fanfiction in this context should stay true to the original personalities of the characters. Sasuke should still be brooding but show growth, Sakura should be strong - willed, Naruto his optimistic self, and Hinata her shy yet determined character. The relationships between them should be well - developed too. If it's a romantic story between Sasuke and Sakura or Naruto and Hinata, it should feel natural and not forced. Also, the setting and the new scenarios introduced should be believable within the Naruto universe.
Well, it could strengthen their bond. Naruto being hurt might make Hinata more protective and caring towards him. This could lead to Naruto realizing Hinata's true feelings for him more deeply, and in turn, he might start to see her in a new light, growing closer to her.
It can strengthen the NaruHina relationship. Since Naruto hates Sakura and Sasuke, he might turn more towards Hinata for emotional support. Hinata's presence becomes even more important to him. He realizes that Hinata is the one who truly cares about him, not like Sakura who is preoccupied with Sasuke.
Well, it could make Sasuke feel a bit left out at first. He might be jealous that Naruto has Sakura's attention. But in some fanfictions, it could also lead to Sasuke realizing that he has some feelings for Sakura too, and then there would be a love triangle situation.
The parents' relationship could also set an example for Naruto and Hinata. If Kushina and Hinata's mother had a strong, loving relationship, Hinata might be more inspired to be as loving and supportive in her relationship with Naruto. Similarly, Naruto could learn from his father's respect for Hinata's family and carry that forward in his relationship with Hinata.
One possible plot could be a friendly sparring match. Naruto and Hinata are one team, and Sasuke and Sakura are the other. They start off with basic jutsu and gradually escalate as they try to outdo each other. There could be some friendly banter between Naruto and Sasuke, and Hinata and Sakura could also have their moments of showing off their skills.