The human ear hears sounds in the range of (roughly) 20 Hz to 20,000 Hz. Musical instruments were designed by humans so naturally create sounds that cover that range. People will argue that regular instruments do not create sounds in that range but the reality is that everything resonates and you get a primary frequency of a note plus a large number of multiples of that primary frequency - and that pretty much gets the highs and lows that we hear. It's the resonances and other generated frequencies that allow us to distinguish between, say, a violin and a trumpet - even though they may be playing the same note.
So, in answer to your question, it is very important that the headphones or speaker system can accurately reproduce the sounds.