Blimey! Sweeping. What about those human hunting bloodhounds and their followers?
I thought about your comment on efficiency. The kill rate of foxhunts was 100%, in that every fox they caught, they killed. They just didn't catch that many. Far, far more foxes are shot than were ever hunted, but with a lower kill rate. A chap called Nick Fox (!) researched and wrote a paper on wound rates from shooting in the early 2000s, and concluded (I think, it's a long and gruesome paper with horribly detailed pathology reports) that somewhere between 12% and 41% of foxes that are shot at are wounded, depending on a number of variables, including gun type and the experience of the shooter.
Shooting is an efficient way of controlling fox populations, but not necessarily a particularly efficient way of killing them. Hunting with dogs is probably not a very efficient way of reducing fox populations, but is a very efficient way of killing them.
I don't have a dog (soz!) in this fight, incidentally. I personally can't abide any leisure occupation that involves compulsorily wearing a uniform. That includes football, golf, foxhunting and game shooting, and I have no desire at all to take the life of any creature, though I do eat them, which I recognise as a moral conundrum.