Consider how some developers today talk about "toast" notifications: they understand on some level that calling them pop-ups is bad, but came to a consensus that using a different name was appropriate, rather than not actually making pop-ups in the first place.
Theme Hospital (a funny 90's game) had a cool way to do notifications, watch on the bottom left as icons pop up: https://youtu.be/26O35BOTVSI?t=693
Some disappear if left unclicked, I guess if the problem is no longer relevant (e.g. a patient bored of waiting leaves), and they can be attended to in any order.
Pop-up ads from the dark ages of the web largely weren't modal dialog boxes. For the most part, clicking to dismiss them, or clicking to bring the window you cared about back to the foreground was at least as easy as getting rid of "toast" style pop-ups. Both are intentionally distracting, neither is blocking in the sense of preventing you from continuing to interact with the window they partially obscure.
