Well, the issue is that anyone who was loyal to Esmenet is probably well and dead. And I don't know that anyone knows who Mimara is, but the good thing is that she doesn't need to dupe anyone, like Kellhus did, she is the real deal. Perhaps they return and find themselves with the Fanim, as Mimara could leverage the Eye as a neat "tool of the Solitary God." Perhaps even find an ally in Meppa.
You're right, of course. There is no established rulership from Esme anymore. Yet, who do the people of Earwa look too, hmmmm?
Akka, just makes perfect sense. Now, many have posed that the majority that hear tell of went down with the rise of the No-God,
will think Kellhus the No-God. What other conclusion could be drawn? He's the only one they know went into the Golden Room.
Akka, plublicy denounced, became a Wizard and made it his life work to find the origins of Kellhus. He survived the Ordeal and rise, he is a Mandate Schoolmen. For that reason alone, who better to trust during the Apocalypse?
If what Zsoronga says is true, many in Zeum believe his book. And, Zuem is the bulwark of the fight against the No-God. That's where Akka & co. head to. Personally, I see no better fit for Akka, and its set up throughout the series. As, someone said, "He's went from most insecure, to obsessed and now fighting what he has been fighting for the entirety of his life.".