Population management is about habitat rather than external intervention.
Example. We had a rat in our garage. We evicted him and made the garage (we thought) rat proof. Rat returned. This time we actually exterminated rat. Another rat moved in. Soooo we removed rat hidey holes from garage and put all edibles eg household rubbish and bird food into metal containers result, no habitat, no rat. Rats are on the increase because modern lifestyle provides an abundant food rich habitat.
You can shoot trap etc foxes, but where there is a sustainable habitat, another fox will move in. If hunts really were an efficient method of controlling foxes, there would be a lot less foxes around than there are!!
So ther you have it, not efficient, not humane and soon, not here!!!!