Yes, it does happen. I'm reminded, though that not everyone is as honestly focused upon as clean kill as we are.
When I was a kid, and not yet old enough to take out the old Crossman .177 pumper without parental supervision, my friend and I would go out with his brother and sometimes his friend to "hunt" squirrels. The kid had this pretty powerful Crossman .22. I couldn't tell you what it was. It was over 30 years ago and maybe nearly a 40 year old gun.
Anyway, during those first several times out, I distinctly remember him taking any shot he could at the squirrel and the 2 or 3 of us chasing it round and round the trees. It would often take 4 or 5 shots to finally bring the squirrel down. The kid never really practiced and was just interested in shooting the rodent. It was a blood lust thing, I think. It was for us, too. We'd chase that poor critter like dogs on a scent. I'm not going to say I didn't like it, either. I think it tapped into something that lives deep in our "lizard brains". Something that we are hard-wired to enjoy because doing it kept us alive for millions of years.
I will say that upon sober reflection and discussion (I took hunting and fishing ethics VERY seriously as a kid) with my friend, we came away feeling that we could do better and should do better, when we were allowed to hunt on our own.
If I'm not mistaken, the next summer, we both got Sheridan 5mm's for our birthdays and we spent two months practicing every day. I'm pretty sure we blew through about 1000 pellets. On a pumper, that's a lot of pumps, too! I must say, we got good. We actually used to practice shooting bugs at ~20 yards. We actually hit them too.
When the squirrel season finally came upon us, we were out the afternoon of opening day. I can distinctly remember the shock at how easy it was for us to make a clean kill. We were so prepared. We'd flipped to see who would take the first shot, and the other guy was supposed to line up on the critter just in case there was a miss or a runner. Such preparation was unnecessary. It was one shot and down all day. I think we missed on two and hit just behind the shoulder and those guys ran feet before falling to the ground. I also remember the other feelings; slight disappointment at no adrenaline filled chase of wounded animals, pride at our shooting, relief at not causing any pain, and this glow of mature, adult, responsibility. Those were nice feelings. I'd say that day, and the day I won my first wrestling match, and one other (

) were the formative or delineation of my manhood.
There's a way that children or animals handle a hunt and there's the way that a man handles a hunt.
I think that's why it bothers us the way it does when we have a bad shot or an unclean kill. We don't want to be the little beasts that we were as children or the beasts that we see other "sportsmen" behaving like. We know we're better than that and we never want to be there. Of course, that it bothers us means that we never will, but it still sucks. We just need to remember that we do everything in our power to be responsible, respectful hunters, and that we simply can't be perfect.
M