Theory: Aizen doesn't have Bankai and it's not a plot convenience, it's character
Every Soul Reaper begins with an Asauchi (a blank Zanpakutō). Over time, the Soul Reaper pours their own spiritual pressure and soul into it, causing it to become a unique Zanpakutō. A Zanpakutō is therefore a reflection of its wielder's soul and develops a personality heavily influenced by them
The zanpakto has a conscience and personality. This personality is highly influenced by that of the user of the zanpakto. traits of the user are transferred to their zanpakto.
For a soul reaper to achieve bankai, their zanpakto must submit to them and wholeheartedly accept them as its master.
A very core trait of Aizen is that he never submits to anything, he wants complete freedom, he even states that his life's purpose has always been to extinguish those who try to control him. He doesn't want himself to be subjugated by anyone or anything. Not even the cornerstone of the reality he lives in , the soul king. he will go against the very laws of his reality and Universe and decide for himself how the world should be.
This is Aizen's most central and his strongest trait, which influences his every decision and action.
His zanpakto has this trait too.So kyoka suigetsu will also never submit to anyone, not even Aizen. As a zanpakto is a separate entity from the soul reaper. And since bankai can be achieved after the zanpakto fully acknowledges the user completely as its master Aizen cannot achieve it Because kyoka suigetsu will never acknowledge a master. Aizen understands this , he knows his zanpakto will never submit to him because he himself will never submit to anyone. Therefore Aizen cannot achieve bankai.
Another thing is that Aizen doesn't trust anyone and sees trust as a weakness, a lack in one's own capabilities. Ichigo said Aizen and his zanpakto seemed very disconnected. His zanpakto has probably this same trait and thinking. So kyoka suigetsu does not trust Aizen, it sees Aizen as more of an associate.
So with the kyoka suigetsu not trusting Aizen and not willing to acknowledge him as its master, Aizen cannot achieve bankai.