There are several aspects to any shot on game that absolutely need to be considered.
1. Is it legal to shoot this animal in this place and time?
2. Am I comfortable making this shot under these conditions?
3. Is my weapon capable of making this shot under these conditions?
4. Will my target still be in the same place when my bullet/arrow arrives?
5. Am I as close as I can realistically get?
6. Where is the animal likely to go, if it does not drop immediately?
7. Will I be able to find a dead animal in the terrain it is standing in?
8. Will I be able to recover the animal in a safe and timely manner?
Number one should be a no-brainer, although there are situations where it can be more complicated. Opening morning this year I was hunting in a zone that allowed brow-tined bulls and antlerless elk. The other side of the canyon, 240 yards away, was in another unit and spike bulls only. Still legal on my tag, but you darn sure need to know where the lines are.
Number two requires that you truly know the conditions, all the way from you to your target. They aren't always the same. Randy had a longish shot moved off target in one episode due to winds between him and the target. Fortunately the result was a simple miss on a gargantuan bull. Had the bull been facing the other way, it likely would have been a gut shot and a lost animal. This is why you practice (which is not at all what most people do when they "sight in" their rifles). You can practice without using a lot of ammo, just by practicing dry firing (with a thoroughly checked empty rifle pointing in a thoroughly safe direction, of course). If you dry fire a lot, you may be able to limit your live fire to 100 rounds a year or so, for a given rifle. Or shoot a decent .22 a lot, and pay attention to what you hit and what you miss. I've actually shot out to 1,000 yards a fair bit. I am confident I could hit the first shot at 600. I'd never take a shot on game at over about half that, though. I'm comfortable at 200-250. Maybe a little bit longer with a good solid rest (bipod on solid ground, prone position). I shoot out to 400 when I practice, just so I'm confident at 250.
Number three means you know the ballistics of your rifle, you know exactly how it groups with this ammo, you know how wind drift affects point of impact, and you know your bullets will perform properly on game.
Number four is something most long range morons don't consider. If you are shooting at extreme range, your projectile, whether it be bullet or arrow, will be in the air and out of your control for up to a second. Deer or elk can move quite a bit in a second.
Number five. Come on, you're a hunter, not some kind of TV assassin. So hunt already.
Number six is not only about a wounded animal heading onto private land where you don't have access. It also reflects the possibility of one running over the ridge out of your sight, into really heavy cover, or into water. You can blood trail under most conditions, but the further your shot, the harder it becomes to get on the blood trail right away. Rain or even blowing snow can obscure a blood trail almost immediately, and if you can't be there within a couple of minutes you may never find it.
Number seven is tricky. Sometimes it's easy- a bull elk out in the open, a whitetail in a hayfield. Sometimes it gets tougher. A pronghorn in a seemingly endless waist-high sagebrush flat, a muley in one of a hundred identical little openings in aspen regrowth. In some places you can walk within a few feet of a dead animal and not know it. In those places, you had better be closer so you can limit the potential area to search. The majority of shots on game are taken in low light, when light conditions are changing quickly. Unless you have a buddy who can stay where you shot from and vector you in, it may be almost impossible to find the exact spot where your target was standing from a long way off. It will look different in different light.
The last one involves a number of possible factors. Out west, many shots are across canyons. If you have a substantial stream at the bottom, it may be impossible to get to the other side. If you crossed the stream on a fallen log or some such, great. How will that work with a full load of meat? In the dark? Fourth load? I had a once-in-a-lifetime elk license in North Dakota a couple of decades ago. I walked in four or five miles from the truck and found a dynamite spot in dark timber, above a wallow, that literally reeked of elk. The temperature was in the nineties. I walked back out. There was no way I'd have been able to recover an elk safely under those conditions. Even disregarding the very real risk of heatstroke, there was no way a completely inexperienced solo elk hunter was going to get an elk quartered and pack out more than maybe one quarter before it spoiled in that heat. I did the same in the West Elk Wilderness in Colorado, the first time I ever hunted elk. I found a burn with good elk sign, but it was 200 vertical feet below the road and nasty with blowdowns. I didn't have four wheel drive at the time, and getting stuck way back in there after dark with snow coming in would have been life-threatening. Again, no way I could have recovered an elk safely.