If there are many songs on the player, and many by each artist, then giving the full song list when choosing the artist may give a huge list that is not easy to navigate through. Giving the album names instead makes the list sizes more manageable.
I hate the whole idea of navigation by tags, and want the option of navigation by folders instead. By using folders, one can tailor make the arrangement of files to suit their needs, rather than being forced into this artist/album structure. Tags are most frustrating when there are slight variations in tags, and some music is in a different place because of it, or if some tags are missing, and the music is on the player but unreachable.