1. lets clarify what is meant by "kill" "wound" and "kill slowly" - here is what happens when you are shot with an m-16: you stop fighting and die. here is what happens when you are shot with an AK-47 (30 cal round): you stop fighting and die. the difference is, if you get shot with an AK-47, you die pretty quickly and relativly quitly. if you are hit with a 5.56 round, you die pretty noisily, disrupting your friends and causing a medic or two to try to save you. my understanding was that one of the main reasons the 5.56 round was developed was the idea that you could take 3 people off the battle field with one hit - the target and 2 people who were helping him. honestly, the situation is such that the 5.56 is used by countries that care about their wounded, and the 7.62 is used by people who care less about their wounded, so it is not as effective an idea as it may have been.
2. you have to look at what came before - the M-1 Garand fired a clip of 8 rounds, each about 2 or 3 times as heavy as a 5.56 round. each soldier would carry maybe 80 rounds or so. the range was huge, maybe 3 times the effective range for the M-16, and the killing power was huge (these are not AK-47 rounds, they are more like the rounds used by a platoon strength chain fed machine gun). these were almost impossible to shoot while running, but were fantastic for defence. my father used one when he was in the army, and when we discussed how they were used, the procedures were totally different from how one uses a 5.56 rifle.
3. my understanding is (this is what I was tought, and tought others) that after wwii and korea, the US army wanted a weapon that was less robust than the M-1, with the idea that individual soldiers usually only fired a few dozen rounds in combat, and it was cheaper to make a gun that would only handle a few hundred rounds and that could be replaced as needed; was very light (having carried a Galil rifle, with follows the AK-47 design, very robust, but uses 5.56 ammo, I can tell you the m-16 feels like a feather);and had light ammo to allow a soldier to carry 250-400 rounds of ammo; and would be less lethal - with the idea that you could create havoc and use up resources by wounding more people rather than killing them outright. having witnesses a large number of people killed by a 7.62 maching gun round, I can say that they don't make much fuss - they just die.