I think the first example is pretty good:
> Build targets clean, depends, all, without occupying the terminal
This accommodates a workflow where one wouldn't prefer to just open up another terminal to do other stuff (maybe you're not in a graphical environment, maybe there's no tmux, etc.). With just the shell features, one could do `make ... && make ... && make ... &`, but that would cause bothersome output that would prevent you from effectively working in the same terminal. One could redirect the output of those commands, but then you lose it, or you have to think of where to collect it. This provides an alternative where you can background and still have convenient access to the output when you need it.
The other use is something like:
$ nq mpv $youtube_url
$ #work... work... work....
$ nq mpv $next_youtube_url
so that the next starts when the first finishes.