After we depose the Pope (If we do), which both Aymeric and Haurchefant like being men of faith and all, why wouldn't they betray us?
Since when does being faithful translate into being a backstabbing guest-killer? Yes, some (many) Ishgardians are devoted to the point of being blind, but Aymeric and Haurchefant (and by extension Lord Fortemps, I assume) don't seem to be. I think they've shown us that if it was proven that their leader was corrupt to the point of needing to be removed, they would side with those fighting for the good of Ishgard as a whole. And that, right there, is the big thing about Aymeric: he's loyal to Ishgard, not just the Pope. It's just as things stand right now, they're basically one in the same.