I'm not sure what you see as high fantasy? I thought the closest we've ever gotten to what I would consider high fantasy in this series is, say, Descent or Trespasser - but then I look to that idea as very tied to Tolkien, and therefore being supernatural and mythical in nature. Not, basically, Conan.
I haven't played Tresspasser or Descent, but I'll like your post anyways. Because the main game is a high fantasy template too. Especially, as you say, compared to Conan. But then, most fantasy writers aren't influenced by Howard.
Even the plot, on an abstract level, is the same thing... the fellowship, the one ring that causes anguish and a great mission thrust on someone (the rift mark), the dark lord taking over the world.. This is every high fantasy plot.
DAO had high fantasy trappings, but it avoided the main gist of it with the Origin stories.. and with Ostagar. You're just a soldier where things went belly up. And your motive for continuing the Warden mission is varied. Maybe your character feels guilt or needs redemption, maybe they're a Cousland and the last of their line, maybe a CE who just wants to get his family safe, or maybe they're like Morrigan and see an opportunity for power. There's no Chosen One thing going on either way. And the Archdemon is less important than Loghain. Which is far more interesting.