There are songs from OSTs, or even full albums by bands or singers in the anime, that I have never heard in the anime. Some music albums for which this is true:
Le Portrait de Petit Cossette Original Soundtrack — the song my love, so sweet is never used in the OVA.
Keep the Beats! by GirlDeMo.
God only knows -Secrets of the Goddess- — the full version that is 11 minutes longer than the one used in the OP of The World God Only Knows: Goddesses!
Why do they do this? For fan service? To make us feel like the bands or singers are real artists? Or to get more profits from CD sales? In which case, couldn't they have just picked the cheaper alternative of selecting some existing songs that are good fits for the anime?