The story would take a very different turn. The dynamic between Naruto and the rest of the characters would change. For example, Naruto might become more focused on protecting the village without the distraction of Sasuke. His relationships with other friends like Sakura might also be affected. Sakura might be disappointed in Naruto at first for giving up, but then they could bond over the loss of Sasuke in a different way.
The ninja world's power balance could be altered. Sasuke, without Naruto's interference, might grow even more powerful in his dark ways. This could lead to new threats emerging. On the other hand, Naruto, free from his pursuit of Sasuke, could develop new skills or form new alliances. He might start to explore other aspects of the ninja world and become more involved in diplomatic affairs to prevent the chaos that Sasuke could potentially cause.