I think it might be because the plot wasn't developed in that direction or maybe there were other factors influencing his thoughts that weren't shown clearly.
Maybe the author wanted to create some suspense or surprise by not having Byakuya think of that at first. It could also be that the circumstances didn't allow him to consider it at that moment.
Well, it could be that Byakuya was preoccupied with other matters and simply overlooked it. Or perhaps there were hidden details that weren't made obvious to us readers.
Another theme is the exploration of their powers in unique situations. For example, some fanfics might have them team up against a new and powerful enemy, and the story focuses on how they combine their abilities to fight. It can be really exciting to see how their different fighting styles work together.
You could also join some dedicated Bleach fan forums. Fans often share and discuss their favorite fanfics there. They might be able to point you directly to some great Byakuya Yoruichi fanfics. They could even recommend some that are based on specific story arcs or themes within the Bleach universe.
A common theme is their past connection. Given their history in the Soul Society, many fanfictions explore how their past acquaintance and the events that happened between them shape their current and potential future relationships.
One great place to find Byakuya and Yoruichi fanfiction is on fanfiction.net. There are numerous stories there that explore their relationship in different ways. Some might focus on their past interactions in the Soul Society, while others could be more about what - if they had a chance - their future together could be like.
There might be some very niche or creative fanfic writers out there who have come up with this idea. However, it's not a common or mainstream concept. You would probably have to search through various fanfic platforms dedicated to both Naruto and Bleach to see if such a story exists. Maybe on websites like Fanfiction.net or Archive of Our Own.
One main theme could be friendship. As Byakuya, who is from a different background, interacts with Naruto and his friends, new bonds are formed. This theme of friendship across different 'worlds' or character origins is quite common.
Well, in some fanfics, Batman might not take Robin for various reasons. One could be that the writer wants to explore a different dynamic in Gotham without the traditional Batman - Robin partnership. Maybe they want to focus on Batman's solo adventures more, showing his loner side and how he copes with the city's crime all by himself.
Maybe in that fanfic, the writer wanted to explore a different dynamic. Batman might be depicted as being too jaded or having some dark secret that prevents him from taking in Robin.
Madara Uchiha could be a great antagonist. He could have somehow gained the power to cross into the Bleach universe and is causing trouble there. Yoruichi and Naruto would have to put aside their differences and combine their skills to stop him. Madara's powerful jutsu and his desire for power would make him a formidable foe for the duo.
Well, perhaps in the fanfic, Naruto and Yoruichi are brought together by a mysterious force that binds their destinies. They might start off as strangers but gradually learn to trust and rely on each other. For example, Yoruichi could be on a mission in the Naruto world and Naruto helps her out. In return, she offers to train him in stealth and agility, skills she is highly proficient in.