Great detailed review Xracer! I agree with you on three points:
The hotel is not set up for children, so if there are multiple noisy children, there is NOWHERE TO GO. Other resorts like Amankila or Amanpulo have multiple pools/beaches, at Amangiri there's the one.
The room setup allows sound (and a careless eye) to easily wander. With our patio doors open we could hear other rooms. Also, I quickly learned that if I wanted to sunbathe on my patio, I should be as decently dressed as if I were in the main area.
The excursions were $$$. Nothing seemed under $500! We loved hiking the trails and would have liked to do the guided piton hike, but the price was just too high!
That said, I loved Amangiri, and would like to go again (on a low level child weekend). I wonder if it will eventually go the Post Ranch Inn route and ban children entirely.