In an X11 window manager, the classic use case is "printing the title of the window in its titlebar". Programs like Firefox put the current tab's title in the titlebar text, which can have any random unicode in it.
Actually, that's an interesting question - in wayland, I think it's common to just say that windows have to draw their own ("client-side window decorations"), so the compositor could just... not handle the window titles at all?
