I have that setting on, but it's not enough. A lot of times I play with headphones and if I'm just browsing the web, I take off my headphones so I can't hear the sounds. Even when I can hear the sounds, there's a couple of sound effects that sound identical to the duty pop sound, and it plays rather frequently if you're in a crowded area like a city or revenant's toll (I want to say it comes from people crafting, I'm not sure). The other game sounds can also drown out the sound of the duty pop sound. There are also plenty of reasons why you would mute the game sounds while browsing the web, for example watching a youtube video or something on netflix. Basically even with the sound, you won't always notice when the duty pops.
Ideally you'd want something like the client to flash in the taskbar when duty pops, or even force the game window to maximize when duty pops. A lot of windows applications can do this. I'm no programmer, but I would imagine that it's possible for square-enix to do it too.
