Piccolos are the highest pitched, shrillest instruments - and I think that's probably why Elder Wirthlin chose them to use as the example of the instrument God doesn't just value in His orchestra. ("Concern for the One")
It's important to have piccolos in the orchestra if you want the full range of sounds, since nothing else emits that particular sound, but it's just as important to hear the other instruments playing. The fullness of the Gospel isn't understood, in my opinion, unless all the instruments are playing together and in tune - and I see "unity" as a fullness of harmonic sound, not everyone playing the same melody. It's up to those who play the instrument that is in the largest section and tends to dominate in volume to allow all the other instruments to play, be heard and feel appreciated.
I've heard the full harmony played in a ward in which I lived, and it's a gorgeous sound.
Christ as a Sanctuary or a Stumbling Stone
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