In general, especially when it comes to using DSLR cameras, it's usually unwanted. It's the same as when the volume on an audio system is up all the way and you can hear the white noise. Most musicians wouldn't want that in most of their songs, but I can understand if they were trying to aim to a specific genre, sound, or theme of their songs.
I agree, 99% of the time when I'm shooting I do not like noise in my pictures, especially when I'm planning on using that shot in color. I'm just saying noise isn't the devil and can be interesting if utilized correctly.