Well, 2nd and 3rd order harmonics at the top of the audible range, and even higher for psychacoustics (sensed not heard), are a very real qualitative element of music. A major one ? no. Especially not for avg. consumer. They impart a certain sound, or better yet, a certain effect on the corresponding freqs below. Sweet, rich, warm, are all adjectives that have alot to do with high frequency representation/saturation, not just bass/low mid freq. there are of course certain necessary curves and dips for phones that are not required for speakers.
But keep in mind there are reasons why the pro audio circuit pays large sums for old pieces with terrible numbers (very high levels of harmonic distortion, etc.)
Also, the statements about MP3 kbps qualitative perceptions are strongly rooted in these concepts.
Above 13k is important, without doubt.
BTW, if you can hear your old TV's tinny whine, you can hear well above 15k.