Strip away the anime and supernatural stuff and Death Note is a 1950's detective cat and mouse where both the protagonist and antagonist switch depending on who's got the current upper hand, lol.: Sherlock Holmes where a large amount of it is taken from Professor Moriarty point of view.

With a long history of crimeprocedurals on both the big screen and the small screen you figure that would be the part they nail, but they never do.