Here not running Deer is one of the first lessons a hunting dog has to learn. The main reason is game has value, it is a resource and public land hunting just doesn't exist here. The game belongs to the leaseholder or another authority if State or government lands. The leases aren't usually all that large and the likelihood of a Dog running Deer onto another's property (at which point it becomes his or hers Deer) is high. Another reason is the chance of a dog injuring a Deer without a kill is high.
One reason they dock a dogs tail is a sign that it is a hunting dog. Accidents happen, not many Hunters here will shoot a rambunctious hunting dog, no training is perfect. Nonhunting breeds are fair game if trespassing, though any hunter that would actually shoot one are few and far between. Few better ways to start a blood feud than shooting somebodies dog, justified or not.
I shot and docked a German Shepards tail with my .308, I was actually aiming for his tail but was really surprised I made the shot. It was the third time I'd caught that dog running my Deer and I'd warned the owner twice.
You need a lot of open country with few roads or highways to dog deer. The chase can last for miles. Dogs getting injured is common. I've dogged Hogs before. Dogs get ate up with the chase and lose all common sense, sharp sticks, barbed wire fences, Gopher holes. But I have to admit the chase is fun for the dogs and the hunters.