Besides naturally-sourced pharmaceuticals, what objective benefits do biodiversity offer humans?
Additionally, I'll mention that I agree with blaabjerg's response: it's worth maintaining biodiversity for the fun of it.
See, for example: http://en.wikipedia.org/wiki/Trophic_cascade
You can use "incredible complexity" on literally anything. Everything is complex. Humans manage.
Corollary: I don't see how a broadly conservative approach to managing biodiversity can be discounted because it isn't specific enough.