Sasuke could be sick of it because he values Naruto's strength and potential. He knows that Naruto is important for their village and for their future battles. Sakura hitting Naruto could potentially harm Naruto physically or mentally, which Sasuke doesn't want as it could affect their overall power balance and the future of the village.
Perhaps a bigger threat or a common enemy could emerge. This would force the three of them to work together more effectively. Sakura would then realize that hitting Naruto is counter - productive and Sasuke would be glad that the situation has changed. For example, if a powerful new enemy attacks the village, they would need to focus on defending it together rather than internal squabbles.
Well, Naruto has a very warm and persistent personality. He's always there for his friends, and he has a big heart. In fanfiction, Sakura might see these qualities in Naruto and realize his true value. He's the kind of person who can make her laugh and feel safe, which could be very appealing compared to Sasuke's more brooding nature.
Sakura's ability to forgive and still care for Sasuke despite his past actions could also make him proud. In many fanfictions, she represents unconditional love. This selfless love and her ability to see the good in him, even when he was at his worst, could make Sasuke proud of her as a person.
The dynamic would be turned upside down. Sasuke would likely become more of an outcast or a loner, feeling rejected. Naruto would be in a difficult position, having to balance his friendship with Sasuke and his new relationship with Sakura. Sakura would be the catalyst for this change, and she would have to face the consequences of her actions, like dealing with the villagers' opinions and the potential backlash from Sasuke's supporters.
Maybe Sasuke sees Sakura's growth as a kunoichi. She has become strong and independent, and he admires that. So he wants her to be his.
Well, perhaps the writers feel that the Sasuke - Sakura relationship in the original was a bit forced. So they create fanfiction where Sakura doesn't love Sasuke to explore different relationship dynamics and character arcs for Sakura. For example, she could have a more platonic or even antagonistic relationship with Sasuke, which would be a fresh take on their characters.
In the Naruto fandom, such a fanfic would be very out of character for both Naruto and Sasuke. They are comrades and friends with Sakura. However, some dark or AU (Alternate Universe) fanfics might explore extreme and unorthodox ideas. But in the main canon, they would never do this as they have a deep bond with Sakura. Naruto has been friends with her since childhood and Sasuke, despite his aloofness, also values her in his own way.
Sasuke might kidnap Naruto because he wants to prove his superiority. By taking Naruto captive, he can show that he is stronger and more in control. It could be a power play, where Sasuke is trying to assert his dominance over Naruto once and for all.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
In some fanfictions, Sasuke might be a jerk to Sakura because of his brooding and solitary nature. He has his own goals and demons to fight, and sometimes he may push Sakura away as he doesn't want to involve her in his dangerous world or be distracted from his revenge. Also, his pride and the sense of superiority he has developed over the years could make him act coldly towards her.