In Bleach, a Soul Reaper must successfully complete one of three processes to become a Captain. The first of these—the Captain Proficiency Test—is the most typical and widely regarded. This entails achieving and activating one's Bankai while demonstrating a high degree of battle prowess and skill in front of at least three Captains. It is significant that one potent Soul Reaper was left out given the series' frequent Captain changes and the intriguing choices of the newly appointed Captains by the finale.
For many years, Renji Abarai served as the 6th Division Vice-Captain, reporting to Byakuya Kuchiki. Renji had progressed from a high-level Vice-Captain and achieving his Bankai in the "Soul Society" arc to Captain-level in the "Fullbringer" storyline as the Thousand-Year Blood War progressed. He was arguably stronger than the bulk of current Captains by the time of the second Sternritter invasion. Renji could easily surpass the Proficiency Test or even the less popular third technique of slaying a Captain in single battle. So why does he continue in his position as Byakuya's right-hand man?
Renji Abarai is Devoted to Byakuya Kuchiki
Renji initially wanted to surpass Byakuya, a goal he had set before even entering the Gotei 13. As time passed, their bond grew strained and resulted in conflict. Yet, upon Byakuya understanding the importance of family and his relationship with Rukia at the end of Bleach's "Soul Society" arc, the pair tightened their bond and strived for similar goals. Because of this joint understanding and Renji’s vow to surpass his Captain, remaining in his current position allowed him to continually be below the one he wanted to surpass. Having Byakuya as his Captain continually pushed Renji to grow -- which is what the latter wanted.
A similar dynamic can be found in the relationship between Kenpachi Zaraki and Ikkaku Madarame, which is explored more thoroughly in regard to the rank of Captain. Renji is in fact the one who suggests that Ikkaku take the Proficiency Test, but the 11th Division 3rd Seat refuses, citing his undying loyalty to Kenpachi and singular desire to fight and die under his Captain. Due to Ikkaku’s motivations, the rank holds no interest for him. Renji seems to adopt this mindset further into Bleach. His ambition shifts from beating Byakuya and becoming a Captain afterward to continually growing in strength and as a person -- with Byakuya as his leader.
Renji possesses all of the strength and skill of a captain; he simply lacks the desire.
At first glance, two of the three Captains selected following the Thousand-Year Blood War seemed like unusual picks. But, when we look at the characters in question, and assume they gained enough power to reach Bankai and compete with the likes of the other Captains, their ascension makes sense.
Tetsuzaemon Iba shared Sajin Komamura's loyalty and had a close relationship with his division. If he got to Bankai, it made perfect sense for him to become the 7th Division Captain. Lisa Yadmaru has little screen time in Bleach, but she is nonetheless considered a veteran among the Soul Reaper ranks and was once the Vice-Captain of the 8th Division, making her a strong candidate to replace Shunsui Kyraku.
Should Byakuya leave his position of 6th Division Captain by whatever means, Renji would be the first choice to replace him. He does not lack the qualities to become a Captain; he simply lacks the desire as his ambitions can only be achieved by serving under Byakuya. Renji feels he can grow stronger by looking up toward the man he wishes to surpass, rather than standing on an equal footing with him. As long as Byakuya remains a Captain, Renji will be his loyal right-hand man.
