Indeed!

That is no baloney.

On the farms where the rifle is discouraged, it is replaced by the lowly shovel that is put to work filling holes. Elsewhere both are used. In fact, we used a waterwagon to swamp holes, shooting the soggy groundhogs with a revolver when they crawled out to escape the water. And also used flex-pipe shoved over a pickup exhaust pipe, the other end being shoved down into a chuck hole. Escaping smoke identified the connected holes and then all but one of those were then plugged and th rig left running for "awhile" {technical term}.

As for the "finishing shot" concept, some fellows I know carry a download or cast bullet load for their rifle in their pocket, or a pistol to finish off a squirming critter. I rarely have a handgun with me when I have a rifle along but I do frequently have grouse loads that would suffice for such a purpose, but I can't remember ever actually using such a load for a coup de grace. A regular high power load to the back of the neck has been it if necessary, but that is uncommon.