Well these days the chances of bells, visual or audible, getting through are less and less, e.g., https://github.com/alacritty/alacritty/issues/1528 and on chromebook one must turn the bell on, etc.
So I still think something different should happen than each forlorn character just mounting up on the screen. Just like when the recycle department doesn't just let one pile stuff up at their door when they are closed.