Well, Deku's arm loss happened when he faced an adversary whose abilities were beyond what he could handle. It was a high-stakes moment that had a huge impact on the story.
It might be for Naruto's own good. Sasuke may believe that Naruto is on a dangerous path that will lead to his downfall. So he captures him to keep him from making bad decisions, like sacrificing himself for the village or something similar. He wants to save Naruto from himself in a sense.
In some fanfictions, Naruto might reject Sasuke because of Sasuke's continuous pursuit of power in a way that endangers others. Naruto, who values friendship and the safety of the village, could see this as a betrayal of their shared values.
Naruto might protect Sasuke by using his physical strength. He's got those powerful jutsus like the Rasengan. If any enemy comes near Sasuke, Naruto can just blast them away with his attacks.
Yes, there are such fanfictions in the Naruto fanfiction community. Some fans like to explore unique and creative scenarios in their writing, including this rather unexpected one.
I'm not sure if there is such a specific fanfic. Fanfiction can cover a wide range of scenarios, but cheating themes might not be very common in the Naruto fanfic world, especially considering the strong bond between Sasuke and Naruto. However, with the vast amount of fanfiction out there, it's possible that one exists.
The 'naruto rejects sasuke fanfiction' alters their relationship drastically. It takes away the hope of reconciliation that is often present in the original story. Naruto's rejection could push Sasuke further into his dark path, making him more bitter and vengeful. For Naruto, it's a difficult decision that might haunt him, but he feels it's necessary. This new state of their relationship means they no longer have each other's backs. Their connection, which was once so strong, is now broken, and they are likely to be on opposing sides in any future encounters.