IMO the problem with the 5.56 round is its relatively low power and small size. This was intentionally selected so troops could carry more ammo.
I have read that the older M193 round was considered "inhumane" as it would fragmentate upon impact (due to its super high velocity). It directed its energy into the target as opposed to the M855 round which was designed to better penetrate a steel plate at 400 yards.
My point then is this, the 5.56 mm round is not low powered. The M193 projectile hits a soft target and explodes createing a tremendous wound channel. The M855 ball round was designed to penetrate a 10 gauge steel plate at 400 yards and it does so. That is not a characteristic of a low powered round either. Both rounds encompass the realization that the modern field of combat does not typically require one to regularly engage point targets beyond 500 meters. So, at the distances the round is designed to work at, the 5.56 mm round is effective. It is not as powerful as the 7.62 nato round of course so it will not penetrate vehicles or other hard cover nearly as reliably as the M80 ball round; on the other hand, a soldier can carry a lot more rounds which improves his chances of shooting more enemy soldiers. It's a trade off, as always.
I wound be interested to see a data table of "one shot drops" versus "one shot got up and kept shooting back" for the 5.56 round in Iraq and Afghanistan.