It has to do with the mystery of life, and the immense reaches of time over which life has evolved, and the magic, majesty and elegance of evolution itself. It has to do with a deep emotional response to beauty or ugliness, uniqueness or commonness, strength or fragility, scents and stinks. It has to do with the miracle of DNA and gene expression and selection, and the incredible convolutions of extended phenotypes that makes any definiton of species a little wobbly at the edges. Frankly, the efforts to define biodiversity seem to me almost as futile as efforts to define God.
Biodiversity is emanent, immanent, ineffable.
We need indicators that matter to people. We also need indicators that matter to what it is we are trying to measure.