Why do we want to hear vibrato?

Branching off this question about vibrato, can you musicians and vocalists tell me what, exactly, vibrato adds to music?

As a listener I recognize and appreciate the effect. I listen to classical music—instrumental, orchestral, and especially opera—so there is plenty of well-delivered vibrato in my life. I don’t need an explanation in terms of what I hear. What I’d like to know is why it enhances a note. Oscillating approximation is not pleasing in other art forms: you want your line to be clear and sure, whether in art, dance, or poetry. Why is that pulsing alternation in pitch part of the beauty in music?