The mage/templar conflict will carry on as a main underlying focus I suspect. As you said, a final quest from a final game may allot people to outright destroy the Chantry. Personally, I don't need to be Anders. I'd rather keep them around, powerless. Like the Patriarch from Mass Effect 2.
As for how they'll handle the Inquisitor, we know that he or she will be able to support or even recruit factions iirc with the choice being up to the player. The people will more than likely react differently to each Inquistor. Like a Dalish Mage or a Human Warrior. Though I don't believe that Bioware will go too far out of their way to underline the distinction as it relates to the narrative plot. Will probably involve a lot of hand holding and 'proving yourself' to win powerful people over, as always.
I was referring to how Bioware will handle the Inquisition after the end of DAI, on its role in Thedas.
Either the Inquisition will dissolve at the end of this game or the next, it will be a new international organization like the Grey Wardens but who regulate magic (as the tears in the Veil show that it does need some management), or it will become an underground group that pops up when needed.
I really hope it won't vanish. It wouldn't make sense.
Though I think the Inquisition's presence in southern Thedas, with All the problems in dealing with the different choices, might be a reason to go on the Northern part of the continent.