If we're honest, the harmony in play means that each note is different dependant on the chord. We could argue that we should write something different for each possible combination of note and underlying chord.

That's stupidity. The aim of written music is to give you the basic idea. Your musicality should do the rest - no matter what genre you're in. The fun thing that you can imagine is that those without music tend to be much more harmonically pleasing because they aren't thinking "must play/sing C".