I have a strong memory of being 12 years old, lying awake at night with the melancholic feeling this article describes, with the realisation that those beasts never did anything to me and I was essentially going out of my way to trick and slaughter them.
No other game has invoked that feeling in me since. It's a very special game. It remains one of my favourites and a stellar example of what the medium can achieve.
Taking shots on animals living their life in the forest and on the fields imposes a moral/ethical question, especially if you are not being attacked or would otherwise starve to death.
Assuming the deer were in such a social structure to begin with, they'll be alone for maybe a day before another stag steps up. Deer do not exist in a gender ratio of 6:1.
There also are plenty of cute-animal mobs that weren't going to bother you unless you started something. An example that still stands out for me is the first set of sleeping bears in LOTRO.