Tengen Uzui, the Sound Hashira from Demon Slayer, was one of the main features in the Entertainment District arc. He was one of the earlier Hashira to have a feature after Giyu Tomioka in Season 1 and Kyujuro Rengoku in the Mugen Train arc.
Uzui, who was famously known for his flashiness, often showed tendencies to make hasty decisions. One such decision was made during the Entertainment District arc. If Tengen had taken Aoi and Naho to the district, it might have cost him his life, majorly affecting the main narrative. Here is a theory of what could have happened if the decision wasn't altered.
Disclaimer: This article solely reflects the author's opinions and may contain spoilers from the anime/manga.
The casual mistake Uzui was about to make in Demon Slayer that could've changed everything

In the first episode of the Demon Slayer: Entertainment District arc, fans were introduced to Tengen Uzui, the Sound Hashira. Upon the Corps receiving demonic activities in the Entertainment District, Tengen was assigned to investigate. The Entertainment District, strictly allowed only female inhabitants.
This made Tengen decide to take Aoi and Naho from the Butterfly Mansion. While trying to "kidnap" them, Kanao intervened, followed by Kiyo and Sumi. As they were hassling him to let them go, Tanjiro arrived on the scene. However, upon learning Naho was not a member of the Corps, Uzui let her go and decided to take only Aoi.
When Tanjiro requested that Uzui take him, Inosuke, and Zenitsu instead of Aoi, Tengen agreed and spared her. Now, here is where things get interesting. What if Uzui had not listened to Tanjiro's request or Tanjiro didn't arrive in time to intervene? Tengen would have taken Aoi with him to infiltrate the Entertainment District. There are a few problems with that possibility

Firstly, no information was earlier released about an Upper Moon demon being present there, only about some demonic activity. As revealed in the series, Upper Moon demons are one of the most powerful entities from the series, especially for one Hashira to handle. It is safe to say that Aoi wouldn't have been much help given her experience with battle.
Moreover, as later revealed the demon was Upper Moon Six- Gyutaro and Daki, two demons rather than just one. Both have been reported to have killed several Hashira in the past, making it an impossible situation for Uzui to handle alone. If Uzui were to face them alone he would've died.
Tanjiro's intervention may have saved Uzui's life in Demon Slayer: Entertainment District arc
Tanjiro joining Uzui may have just saved his life as seen from instances in the anime. For defeating the Upper Moon Six demons, they both had to be beheaded simultaneously. It was only made possible when Tanjiro aided Uzui to behead Gyutaro, while Zenitsu and Inosuke jointly dealt with Daki. Uzui achieving this alone, no matter how strong he might be, was impossible.
Moreover, as Nezuko always accompanies Tanjiro, she also plays a key part in saving Uzui from death. Her Blood Demon Art allows her to ignite her blood into flame, which neutralizes and burns away demon-related substances. When Gyutaro inflicted his poison upon Uzui, Nezuko used her ability to save him, keeping him alive.
Final thoughts
Tengen Uzui was going to make one of the most drastic decisions to change the course of the arc, fortunately intervened by Tanjiro. Despite sustaining heavy injuries from his battle, Uzui was alive and later seen working as a mentor in the Demon Slayer series.
The Demon Slayer: Entertainment District was one of the best arcs from early on in the series. The introduction to a full-fledged Upper-Rank fight, some of the best cinematic visuals, a good storyline, and a great display of fight sequences led to the success and popularity of the arc. As the final Infinity Castle arc approaches, fans await in excitement as the series unfolds.
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