Tray bar icon + window-independent process for fetching and notifying on new emails in the background

This feature is seen is excellent email clients (Geary, Evolution Kmail) on the Linux desktop and it pains me to be able to use something like this on Thunderbird (currently you have to keep the main window open and minimize it for convenience in order to be able to keep receiving emails). Is there any major blocker that would explain why this is not implemented?