The 5.56 can kill with one shot and it can wound too. No bullet is guaranteed. The 7.62 maybe bigger but is loses accuracy too quickly at longer than 300-400 yards. The military used to use 30.06 and .308 in battle but switched to 5.56 as a more effective and logisticly effecient round. Those larger calibers did the job, but were pretty heavy in both firarm and ammunition. 5.56 has just as much chance at one stop shot kills as any other similiar infantry round. Skill and training have huge roles in this but dumb luck and sheer coincidence does too, factors like weather, enemy's skills or frame of mind, sweat in your eye, random richochet, etc. Wounded enemy even if he isn't helped off the field is a major morale buster, if he bleeds out even better. You always hear about how someone got shot and kept on coming because it is abnormal and is different from the usual norm of just falling over dead that it makes for a great story and interesting item of chit chat.
As for grunts having notoriously bad shots? As compared to who? Just because some armchair quarterback can pop cans at 300 with his irons doesn't mean he can do the same thing when he's tired, exhausted, underfed, dehydrated, underfire, back hurting from humping too much gear, too far, in too much heat, you got a rock as cover, rounds pinging all around, dirt and debris filling your eyes, people screaming in your ears, adrenaline pumping through your veins, your heart thumping in your head, am I gonna die today? random thoughs like "That rock in my shoe is annoying" I miss my wife", does that kid have a gun? Am I going to go to jail when I get back home if I hit the wrong person? All while you are trying to take good shots and properly identifing the right targets. I'd like to see how you would fare, I think our troops shoot just fine. Combat is not like video games, or expensive classes, or shooting at the range. Some troops can turn a switch and be flawless and some can't. Don't blame the boys doing the dirty work, every aimed shot is gunning for a kill, but it's alot harder than you can "imagine."
I think hunters use larger calibers for hunting because some take those LONG shots and a larger round is the only answer, but the 5.56 can do the job on deer too with good placement and proper knowledge. I thought there was a law about shooting and only wounding large game if it did not die quickly, something about letting the animal suffer (I maybe wrong) as well as having to track an animal for long long distances. I think larger caliber in hunting can make up for less than perfect shots.
The 5.56 is a great round, it does the job and is well liked. Alot of people say I heard this one guy got shot 5 times and was still fighting, or this one guy got in the chest and kept on coming. What about the 15 guys that are dead around him? If the 5.56 was a poor perfomer than I think our troops would have no kills or have won any firefights. There are really strange things a human can do in battle, have a limb blown off and be completely numb to it and can keep coming, or a little nick to the neck and he's done. Wierd crazy things happen for a thousand different reasons and variables, and you can't judge the 5.56 on a singular "story" or comparing it to hunting situation.