Just out of interest, is this culling not comparable to the culling of deer that is commonplace?
I have been to Snowdonia and seen the damage done by overgrazing (by domestic sheep as well as feral goats) 
While I hear what you are saying, I think (quite probably I am biased!) that goats have a level of intelligence and empathy that quite possibly outweighs that of many other livestock. When I lost my first whether, I saw something that changed how I thought. It was pouring with rain - anyone that knows goats, knows that they will mostly leg it at the first drop of the wet stuff into their shed! - not my boys mum, Avocet. She stood strong next to the vet and I while we did all we could to help her son. Once the vet and I had managed to lift him into the shed between us, and only then, did she come in for cover herself. WHile he died and for hours after she cried over him, literally cried. Now for goats to have witnessed other members of their herds being shot at, possibly fatally injured but not killed outright even, I personally believe this to be stressful and inhumane.
we also keep sheep here - creatures that make me bury my head in my hands each time we attempt a simple procedure such as transferring them from a small pen into a big field and they get all confused and homersimpson like bless 'em.
Perhaps my goats are just pampered and spoiled though
