The benefit to them would not be converts among the rifters. It would be the narrative. If this—great evil, threatening the foundations of Andrastian civilization— [ and unseen vague gesture, he's not here to make a speech, someone else do that part ] If it is to defeated by mysterious beings from beyond the Veil with magic they cannot explain, it is in their interest to be able to tell the people—the people who pay their tithes and look to them for guidance—to tell them that we owe Thedas' salvation to blessed agents of Andraste, not to demons they never trusted.

But it would require them to not gleefully spout heresy in public, at a minimum, so it may be a lost cause.