Thanks for posting this, Sarah, I'm so glad we finally pulled the trigger on it! A couple clarifications for everyone:
- The custom header functionality in the Customizer surpassed that of the admin page when cropping was re-introduced in WordPress 3.9, along with media library support.
- WordPress 4.1 has a brand new set of media controls in the Customizer, enabling custom background images to use the media library as well. Now that the Customizer version of backgrounds is also more user-friendly than the admin pages, we can kill off both admin pages for most users and focus on future improvements to these features in the Customizer.
- There is absolutely no reason to create any theme options pages outside of the Customizer at this point. Theme developers should be using the Customizer for all of their options, and the other appearance pages will also redirect to the Customizer in the next few releases as Widgets in the Customizer are improved, Menus are added to the Customizer, and Theme-switching and theme-install is added to the Customizer. Plugins that do anything to the front-end should also use the Customizer for all of their options. As the Customizer becomes more prominent, look for a more front-end-contextual experience moving forward, where the Customizer is accessed primarily from the front-end of the site and can be opened/closed more seamlessly.

You can hide the new deep-links from a plugin by adding some CSS along the lines of `.customize-support #menu-appearance a[href~="background_image"] { display: none; }` (untested).