The most important thing about this is that the Nerevarine leaving for Akavir is just a rumor.Anything could have happened to her and it is the player's choice to decide what actually happened.Maybe she indeed went to Akavir, maybe she didn't want to go there but it happened, maybe she 's somewhere else and this rumor spread.
Just another detail that I remember a moment ago - the Nerevarine also took Kagrenac's tools with her when she left.Check out some obscure text at The Imperial Library for that.
Akavir is a nice setting for fanfiction, though not everyone is interested in it, let alone write some.
Yes, the Nerevarine wouldn't have any reason to go to Akavir but you can always pretend something important triggered the trip - like a secret Blades national security mission which goes wrong, ending with the Nerevarine surrounded by snakemen somewhere near an Akaviri swamp
It's not that our hero wanted to end up like that...no matter how much (s)he disliked those xenophobic Dunmer.