Why don't TV shows include song credits?

Backstory:

Arguably the most famous song from "Ice and Fire"is "The Rains of Castamere,"and The National has performed the Lannister ballad for the upcoming "Game of Thrones" second season soundtrack. "The Rains of Castamere" is about Tywin Lannister's overwhelming victory over House Reyne during the Reyne-Tarbeck Rebellion and is featured at several pivotal parts throughout Martin's novels. Particularly during... no spoilers. Let's just say it's an important number and the indie rock band's sombre sound, not to mention Matt Berninger's low register do it justice. It's not upbeat by any means but it's definitely worth a listen. UPDATE: If it seems familiar, it's what Tyrion has been whistling.