About the space: I was thinking the text could replace the icons on the right hand side for a short while (until the user has had the time to read it).
Emacs displays little notes in the echo area at the bottom of the screen, though those are always (?) triggered by user actions and do not come from background activity. Which also qualifies as "since basically forever", I would say.
Also oftentime there is zero extra space in the menu bar.
Alerts and notifications have followed a pop-up pattern since basically forever in computing.