I just finished reading the ARC version of this thread and I've read this one earlier in the week. People debating whether Kellhus is a savior or not, the extent of his humanity/emotions and listing examples from the books got me to thinking about Akka crashing Kellhus's coronation at the end of the first trilogy. I guess I always thought (when I did think deeply at all about it) that Kellhus let Akka leave and live because of some kind of human connection/fondness for him, probably due to wishful thinking and my own natural inclination to want it to be that way. Does anyone else think that could have been a factor, or did Kellhus see his usefulness as a future tool far outweighing any threat he posed and was in total rational power strategist mode, with no emotion playing a part?
I don't know specifically why, but Kellhus definitely has a use for Akka. It struck me when reading TJE that Vem-Mithriti was titled the Vizier-in-Proxy. Before Akka stuck up his middle finger at Kel, his role was to have been Vizier to the Aspect-Emperor. Now, as you say, if Kellhus had no use for him, why not just kill him and appoint a new Vizier? Why, after twenty years, is there a 'Vizier-in-Proxy' position being held open? I can only assume Kel expects Akka to come back, as he 'foretold,' and kneel - maybe to be re-indoctrinated as Vizier. Again, though, not sure why Akka specifically. Maybe Kel 'unlocked' Seswatha in Akka when he hypnotized him to get the Gnosis. I don't know, but Kel doesn't really need a Vizier. He's already more powerful and knows more than Akka by this point. I have no real answer, but I dodged your question pretty well, I think.
IMO, I don't really think Kel has any emotional attachment to Akka. Like, at all. He was, and still is, a tool for Kel. Unless Kel suddenly acquires real empathy, I just don't see why he would 'care' for Akka.