My problem with Azem isn't that they exist as part of the story. It's that they're connected to the PC. The devs are trying to walk on a tight rope. They don't want to give us too much information about Azem so that players can use their own imagination as to how they want to fill in the blanks. While also giving the character enough to make people go ok I can see the connection.
For me either Azem has future sight or is an us that ended up rejoining back to full and traveled back to a further point in time. In a Rhapsodies of Vana'diel type thing. Which I really don't want until we reach the point in the game's lifespan where talk of putting it into a similar mode that XI is in now. As the devs have taken steps to make it to where even sundered each shard might as well be a clone of Azem. Yet if Azem has future sight then why did that part not pass on? Unless that part didn't attach itself to their soul.
I guess I'm one of the few who picked up before 5.3 that the WoL was more than a familiar soul to Emet. Either its due to my using Japanese voices and English text. Since the English voices don't have as an animated look as the other languages. Just look at the animation differences when it comes to Haurchefant. That and Emet is also trying to drop hints the entire time. Always ending up disappointed as he doesn't want to use the Azem stone to force us to remember. I at least went oh crap we must have been something to Emet when Hythlodaeus drops the new old friend bit after having already said Emet and he were friends.
I know many don't like the whole future sight thing in stories but even what little we've gotten in XIV it acts as the same as any other future sight. In that it's very vague. Now from what I've seen there's two kinds. The kind that no matter what you do what was shown ends up happening. Or you can change what is shown. I personally would rather have Azem have future sight then have it be a fully rejoined WoL that had to grandfather paradox ourselves. Especially when it comes to how they reacted to The Final Days. It doesn't look good if we knew what's going on and chose to stay out of it for reasons.