Jane, just to be clear this is more relevant than just removing an image from the post itself. Because each image has a parent_id in the database they are inherently linked. The most obvious effect of this is when the [gallery] shortcode is used. If you accidentally uploaded an extra photo to a post you need to delete it entirely to stop it from showing up in the gallery.
I just checked and the process of manually deleting an image from a post with the red delete button doesn't change its wp_posts record in the database. I don't think you were implying that it was, but I just wanted to make sure there was no existing way to effect an attachment to remove its parent.
I think the proper language for this action would be something like "Remove from post". If a link saying that was next to "Delete" in an attachment's settings in the Gallery tab of the uploader then most users would probably understand that it would un-attach the image from the post but keep it in the media library to avoid images breaking if they were used in the post.
Whenever I explain the [gallery] shortcode to people I eventually get the response that its annoying that you are screwed if you accidentally upload an image that's not supposed to be in the displayed gallery, especially since there are obvious reasons to do so that aren't mistakes. A thumbnail is the most obvious example but there are many others.
I think this would be a great addition to the media uploader and especially to the built-in [gallery] and its usefulness. Having this exposed would also be generally useful for educating users naturally about the relationship between images and posts, a topic which most users I talk to are confused about in the current setup.
Post-attachment status and information would also be useful in the Edit Media screen you end up at from the Media>Library.