I've been a fan of Tolkien pretty much all my life. When I read The Children of Húrin I found it really dark and full of what seemed to me really wise ideas and expressions. I know Tolkien was a huge fan of Norse and pagan mythology, was there meant to be a lesson behind The Children of Húrin?
I think Tolkien tried to avoid the "moral story" or intentional allegory in his works. They are, in essence, simply myths and stories, a fantasy. Tolkien's story of Turin was directly inspired by the part in the Finnish national epic Kalevala that tells of a hapless hero Kullervo who inadvertantly seduced his sister and both commit suicide. http://en.wikipedia.org/wiki/Kullervo
Having said that, I think the overall thread of tragedies in Tolkien's legendarium (and there are plenty of them in the Silmarilion) are a reflection of how the world, which fell from God's grace, is imperfect and full of failings and suffering. Tolkien's mother died when he was a child, and he had to go through the horrors of the Great War (World War I). This directly influenced his writings. In opposition to that, Tolkien's writings give an idea of the unlooked-for salvation (such as in LotR), or some other kind of redemption. In his early versions of the legendarium, at the End of Days the deified Turin has a battle with Morgoth and kills him permanently with his black sword, thus revenging his and his sister's tragic fate.
Thus spake the prophecy of Mandos, which he declared in Valmar at the judgement of the Gods, and the rumour of it was whispered among all the Elves of the West: when the world is old and the Powers grow weary, then Morgoth shall come back through the Door out of the Timeless Night; and he shall destroy the Sun and the Moon, but Eärendel shall come upon him as a white flame and drive him from the airs. Then shall the last battle be gathered on the fields of Valinor. In that day Tulkas shall strive with Melko, and on his right shall stand Fionwë and on his left Túrin Turambar, son of Húrin, Conqueror of Fate, and it shall be the black sword of Túrin that deals unto Melko his death and final end; and so shall the children of Húrin and all Men be avenged.
The Quenta - The History of Middle-Earth