I recently wrote about things that make me so attached to xterm . One of those things is xterm's ziconbeep feature , which causes xterm to visibly and perhaps audibly react when it's iconified or minimized and gets output. A commentator suggested that this feature should ideally be done in the window manager, where it could be more general. Unfortunately we can't do the equivalent of ziconbeep in the window manager, or at least we can't do all of it.
A window manager can sound an audible alert when a specific type of window changes its title in a certain way. This would give us the 'beep' part of ziconbeep in a general way, although we're treading toward a programmable window manager. But then, Gnome Shell now does a lot of stuff in JavaScript and its extensions are written in JS and the whole thing doesn't usually blow up. So we've got prior art for writing an extension that reacts to window title changes and does stuff.
What the window manager can't really do is reliably detect when the window has new output, in order to trigger any beeping and change the visible window title. As far as I know, neither X nor Wayland give you particularly good visibility into whether the program is rendering things, and in some ways of building GUIs, you're always drawing things . In theory, a program might opt to detect that it's been minimized and isn't visible and so not render any updates at all (although it will be tracking what to draw for when it's not minimized), but in practice I think this is unfashionable because it gets in the way of various sorts of live previews of minimized windows (where you want the window's drawing surface to reflect its current state).
Another limitation of this as a general window manager feature is that the window manager doesn't know what changes in the appearance of a window are semantically meaningful and which ones are happening because, for example, you just changed some font preference and the program is picking up on that. Only the program itself knows what's semantically meaningful enough to signal for people's attention. A terminal program can have a simple definition but other programs don't necessarily; your mail client might decide that only certain sorts of new email should trigger a discreet 'pay attention to me' marker.
(Even in a terminal program you might want more control over this than xterm gives you. For example, you might want the terminal program to not trigger 'zicon' stuff for text output but instead to do it when the running program finishes and you return to the shell prompt. This is best done by being able to signal the terminal program through escape sequences.)