Look in a history book and tell me when anyone besides a Grey Warden has ended a Blight or where anyone who's not a Grey Warden thinks they can. The fact is, no one in Thedas believes otherwise, and everyone in Thedas is correct in that a Grey Warden is needed. You can try to break the mold all you want, but your view is accepted nowhere.
Hindsight's 20/20.
History makes out the Wardens to be this incredibly badass force of Darkspawn-focused warriors that can end the Blight by their very presence, a claim they don't try to ground in reality as we see at Ostagar through their neglect and bare minimum amount of effort in telling Cailan the Manchild that he thinks far too much of the Wardens.
But the reality is they're anything but uber-skilled invulnerable badasses. Certainly more skilled then your average soldier or knight, but not as great as people like Cailan make of them.
The world doesn't know why precisely Wardens are necessary. Only that they're devoted to fighting the Blight and have shown up in every Blight thus far, playing integral parts. Very few people outside of the Order know their secrets, and if we did the DR then I'd imagine even more people would question the idea of "why". In the previous ones, your average soldier could chalk up the Warden's death to injuries sustained in battle (you know, since they're going up against a giant dragon) -- hell, Garahel's corpse was thrown across the battlefield -- since this is a world with limited medical understanding.
I'll admit it's too bad that I have to read the Stolen Throne in order for me to understand why Loghain is the man he is in the games. If that was somehow integrated in Origins It would've prevented me from executing him.
I'd argue it is integrated, though not as well as it could've been. You just have to recruit him, because he's really the only person who could give you that perspective if you don't read the codexes on the Orlesian Occupation.
Bryce is dead, Howe's a slimeball who wouldn't give you the time of day, Eamon and Teagan were sent north, Rowan's dead, and Maric was hooked up to a Dancingian Ouroboros.