Mmmm yes. And Shadow the Hedgehog is way "darker" than Twilight Princess. Edgy =/= Dark.
TP tries to be the "dark" game, but it fails in giving that feeling to most players.
Which is why a middleground is needed. You need light to compliment the dark. It makes the lighter parts that much better, and the scary parts much darker. This is the reason why OoT is way darker than TP could have ever hoped to achieve.
You're certainly right, edginess does not equal darkness. So explain how TP is "edgy." Please, do. This is why I sometimes feel people don't actually listen to the arguments of those they disagree with, because not a single point I made supported TP being "edgy" over being a substantially emotional game with tragic undertones-- in fact, I argued against that-- yet you still seemed very happy to make such a claim as though it somehow nullified my entire post. How?
Darkness is not a "feeling" that you derive from a mood. Something may be "scary", but not dark, not in any substantial way. Darkness isn't horror, or terror. Darkness isn't a drug you turn to for cheap claustrophobia or grimness. You can't see it with your naked eye; it's much more universal than that.
True darkness is scientific. It carries truth and relevance even after you've turned the console off, or closed the book. It can't be cancelled out with lightness or humor, because it's always there, lingering. It's imbedded objectively in the themes and the structure of a work, and it takes careful analysis and understanding to truly extract. OoT lacks this; TP has it in abundance.
OoT is emotional, yes. It's occasionally depressing and even horrifying, and it carries themes of dissolusionment and redemption; but at its heart, it's a coming of age story, about a young boy who goes off on an adventure and experiences how wondrous, and very often heartbreaking, the world is, and that's what makes it ultimately a light game.
TP is different. As a more sophisticated piece of literature, it's focus isn't primarily on Link, but on Midna (as well as many other outlets), and her story is not a happy, or even very uplifting one. The story of her suffering at the hands of Zant, which never comes to any resolution other than her eventual resolve to protect the world(s) at any cost; the story of her people, meant to wither away into oblivion for their sins, and their eventual redemption due to Midna's sacrifice; Zant's weak and greedy soul, his manipulation by his "god", and his eventual descent into utter madness; the solemn and terrible duty of leadership uptaken by Zelda, Rutela, and Ralis, all who suffer dearly for their responsibilities; the struggle and resolve of Renado, Ilia, Colin, and others in the face of adversity, and even death... All these, while inspiring, are ultimately illustrative of heavy and truly dark vision of reality.