What prevents this from being done using a Chrome extension to look at the page structure and render some UI, plus a bit of native code using the native messaging API to actually store the files on disk?
https://developer.chrome.com/extensions/nativeMessaging
"Developer frustration" is a more-than-valid reason, but I'm trying to understand if this is a claim that no software like DownThemAll can possibly be written without Mozilla introducing purpose-built extension APIs.