I was looking back to my own area mid 90's, we don't have fallow or any other herd deer species, and back then roe were a rarity aswell, but I see what you mean. Fields devoid of hares are a desolate place for me
Leaving the catch to rot is a knackers errand, I've known of places where the hares have been shot out, but the other species are still there to run, so never really understood why the hare has to get the shitty end of the stick