I never got this feeling that Aymeric isn't 100% on our side. Certainly he has a few qualities of a Chess Master, but I think he has more qualities of a leader. He's iconic, charismatic, knows how to delegate responsibility and work, and has a good ethic for doing his duty. I can't agree with those who say he's too perfect and hasn't messed up, because he has, quite often, and suffered the consequences as well. There's no need to repeat what others have said about the Vault or the stabbing.
If anything, my guess is that Aymeric is slowly coming to terms with the same advice we get from Matoya; how far are we willing to go? I think Aymeric is asking himself the same question. For the good of Ishgard, what is he willing to do? What morals and values are he willing to compromise? The incident with the child being thrown off the Vault in 3.1 probably shook him up pretty badly. There is a power vacuum in Ishgard right now, with the seat of the archbishop vacant. It's unlikely Aymeric could become the next Archbishop, as I believe they're selected from the Clergy. Is he facing the prospect of taking up the crown instead? Of becoming Ishgard's first King in over a thousand years? He'd probably have an easier time securing the crown than the seat of the Archbishop.
Then there are Ishgard's social problems to contend with. How does he improve the quality of life of the lowborn? How does he rectify that with the highborne? How does he change anything without making enemies of those people who have made a life of rising through Ishgard's ranks as they've existed for a thousand years? Imagine if all the people in the Convictory (I believe that's the dragon hunters in Western Coerthas) were suddenly told their accomplishments don't mean anything anymore and they can just go back home?
I think Aymeric is facing the reality that he has to make personal sacrifices before he can bring about an Ishgard greater than it has ever been before, and that even then, he will be engaged in a never-ending war with his own nation to keep Ishgard great.