What does the phase of a FFT bin of an audio signal represent?
The frequency bin with the highest magnitude is very often not the fundamental pitch frequency, especially for lower (male) voices and larger stringed instruments.  It could instead represent a strong overtone or harmonic.

The FFT phase result is very important in representing any transient waveform shape or timing, for instance whether a note onset or percussive hit occurred toward the beginning or end of the FFT frame.  It's thus not very useful in matching sounds unless the FFT frame timing is somehow very precisely matched to the sound's timing.  

For a very narrow-band signals that are stationary across multiple FFT frames with known time offsets, the FFT phase results can also potentially be used for frequency estimation finer than the FFT bin spacing resolution.