I'm away from my Lorebook at the moment unfortunately, but it's fairly correct that the Ishgardian Orthodox Church got more and more power over time. The Lorebook describes that the earliest versions of the church (and indeed the scripture according to the Scholasticate quests) focus on the 'maternal' aspects of the church such as spiritual guidance, charity, and religious contemplation. The realities of the Dragonsong war, however, gave rise to a 'paternal' aspect involving direct governance, martial skill, and 'justice' against heretics. With Ishgard stuck in a state of Total War for nearly its entire modern existence, a bureaucratic body was necessary to maintain logistics and continue prosecuting the war against the dragons. The Church proved more than capable of this task, and built up the necessary logistical and governing bodies over time, with the Archbishop soon becoming the most powerful figure in the land. It was seen as better for this task due to both its holy status, and the fact that it was not directly aligned with any particular family or group of nobles. However, with the revolutions and new discoveries at the end of Heavensward, the Church's 'paternal' aspect is being heavily dialed back, and the church is going through reforms to emphasize its more charitable, 'maternal' aspect.