I don't know that I would count a countdown as an intro... livestreams are inherently a different beast than VODs. An intro is more of a channel introduction placed at the beginning of every video. They are intended to provide the viewer with the creators background so that they don't need to explain who they are etc throughout the video, but they are often used as simple, time-consuming blocks with little more than a logo as a selling point that their channel is more professional than it really is.
I will say though you provide some interesting points here!