Comment 48 for bug 844081

I'd be concerned that a user might choose an inappropriate desktop wallpaper and I'd have no way to prevent it from being displayed to everyone who uses the computer, so as admin I'd want to be able to switch off the feature of showing the selected user's wallpaper on LightDM and instead only show the same wallpaper for everybody. What people put as the wallpaper on their own account is up to them, but the login screen is a shared space.

Aside from that, as someone who isn't admin I might not want to show everyone my wallpaper. For instance, I use a wallpaper of Humble Indie Bundle 5 which seems childish for my age. I might not want others to see it when they come to use the computer. Now that I've read some of the comment section I know I can hide it with file permissions, but I wouldn't have thought of that on my own even after using Ubuntu for over 6 years. It makes much more sense in terms of organization, intuitiveness, and respecting user's privacy (which I thought Ubuntu was trying to champion) to make it a switch in the Appearance panel:
[X] Show my wallpaper on the log in screen

Which behind the scenes just changes the permissions on the file as described by others. No fancy stuff.