Problem is, 5,56mm ammo was designed with conventional WW3 in mind. Conventional as in WW2, just with modern weapons, in similar environments and engagement ranges, against a similarly equipped enemy. Its main purpose was to wound, because wounding takes more soldiers out from action than killing outright. Nobody certainly expected in the future an extended asymmetric (because guerilla is apparently a four-letter word, as seems to be counterinsurgency) war that is fought in barren terrain with little cover and thus extending engagement ranges to many times greater than those typically found in Europe or Pacific (or Southeast Asia, for that matter). Also, it is considerably more difficult to stop a fanatic who's actually willing to die (preferably taking some enemies with him) for a cause, as opposed to someone who is just "doing his job" and actually trying to survive: while the Soviet economy might have been in shambles, even the average Soviet of the Cold War era had a lot more to lose by dying than the average Taliban of today.
However, one thing has not changed from WW2 is that on average 200 000 (two hundred thousand) bullets are still fired in anger in order to cause one enemy KIA (the main killers being arty, air strikes, tanks, infantry support weapons, hand grenades, and only at the very bottom of the food chain, rifle bullets). The effects of aiming are still negligible, no matter what you are told in basic training: hitting the bullseye "easily" on rifle range (as many are prone to say), or even on manoeuvers in terrain, is very different to a situation where shit just got real, when your heart beats 180bpm, bullets are whistling by your ears, there is an awful lot of noise, explosions, flying dust and debris obscuring the targets, and the enemies are moving, dodging, and taking cover, etc. All that training is just to ensure that when in that 1 in 200 000 situation you are able to take the shot, at other times it's mostly for your own reassurance (plus bullets aimed at the general direction of the enemy are more likely to keep their heads down than those fired into the sky). What really matters is the volume of fire. So having 200 5,56mm shots heading downrange is better than 100 7,62mm shots, the rest is just statistics. Which makes the accuracy and stopping power of 5,56mm round at range rather irrelevant as long as dedicated marksmen and snipers, who are the only ones actually supposed to hit at a distance, have something heavier. Also, just about anyone can reach high ROF with a (semi)automatic weapon, even if taking breaks to let the barrel cool down, whereas the "mad minute" with bolt-action rifles takes lots of drilling and still won't be an easy feat (and the time used to learn this skill, which is made redundant by technology, could be used to learn other skills).