I was going to make a similar point, and I was just considering how I'd put it to avoid speaking out of turn. As I understand it, in the US there's a number of reasons why one might aim to ruin as little meat as possible, including such things as bag limits and limited seasons and limited opportunities. Here in Oz, much like NZ, considerations are a bit different.
Where I hunt, there are no bag limits on deer. For several species there's no closed season either, at least where I hunt, though one might prefer to hunt in the cooler months for practical reasons. You've still got to find the deer though, and some in particular are quite wary and like thick cover. As a result losing a bit of meat may not be such a big factor, and may be outweighed by the benefits of dropping it on the spot, especially in thick bush where you might otherwise have a hard time finding it if it was to bolt. That is my personal reasoning anyway.
Of course in the case of animals which might become aggressive, there's also the argument in favour of putting them on the ground and out of action straight away before that can happen.
I don't know that a lot of deer are simply left in the field in NZ any more. I don't think that is true here either. We don't have "wanton waste" rules though, so there's no particular reason (other than preferring not to waste something tasty) that you'd be prevented from leaving deer, or the bits you don't want, out in the field to rot.
There's a good proportion of other critters left in the field though. A lot more pigs shot than are eaten for example.
