I think handgun shooting, in a sport like bullseye target can be a help to the hunter. The level of concentration needed to get perfect sight alignment is a good practice point.
I shoot running game, I've missed before, and likely will again. To date, I have not knowingly wounded anything. But, I have participated in a number of recovery missions, some that lasted days. Practice makes perfect? Not really, but it helps. Sometimes the perfect shot, just doesn't work out as planned. I also believe in more than one shot, if the game does not fall imediately, or if the supposedly dead game will be out of sight during your aproach, because of terrain. I have had game get up after a shot, in one case, the deer was ten feet from me, laying supposedly dead. The dogs were still running, so I elected to stay in my stand for a bit. After about five minutes, I heard a noise, and turned to see my deer attempting to make his escape on his two front legs. Back broken behind the front shoulder. Head shot ended that quickly.