The Inquisition? [SPOILER]

[Enkidoh]

The Inquisition were entirely connected to the Church, and, given the player kind of destroys it's power base (exposing both the lies the Church was built on, the rampant corruption within the organization itself, and that.. whole thing with the Archbishop and the Heavens Ward...), the Inquisition technically no longer exists in any meaningful form.

They were also well known for working in secret so again it's pretty obvious why apart from that kangaroo court that Alphinaud and Tataru were caught up in (and some lore padding that started the DRK quests off), that the player has actually little contact with them.

[EdwinLi]

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Despite working in secret their lack of involvement is what is questionable. The WoL has made a very large commotion within Ishgard society even before he or she entered Ishgard which such level of commotion should have taking the Inquisition's interests considering the WoL is a outsider that has been chosen to be the 2nd Azure Dragoon, Saved Ishgard in steps of faith, unraveled a false Inquisitor, and etc.

Also, despite the truth being revealed the Church has not falling yet. While scholars of Ishgard are struggling to revise their history currently after 3.0 due to the Truth being revealed there are still some loyal to the church and the old beliefs as was mentioned at the end of 3.0 on how Ishgard can't be changed over a day but by generations and other Side storyline quests