It happens often that users don't properly fill out the necessary data required for images in the media center (especially like alt tags).
To take care of that issue add "required" checkboxes to the settings->media section for:
If e.g. alternative text is checked
-the user is allowed to upload images into the media center
-the user is allowed to select images for posts or custom post types.
-the user is allowed to save those posts and custom post types as draft.
BUT the user wouldn't be allowed to publish posts or custom post types containing images without the required image fields.