The 5.56 is perfectly adequate for CQB ranges, no doubt about it. Any modern rifle cartridge with a "frangible" projectile between 50 and 200 grains and a velocity over 2700 fps is perfectly adequate for CQB.
But even a 30-30 with a 150 gr soft nose bullet will leave a larger permanent bullet wound than any military small arms bullet save OTMs.
The failings of the 5.56 cartridge are not in CQB, the failing is in lethality over the full engagement range of the weapon systems. After about 200 meters there just isn't enough velocity/energy to cause 5.56 fmj bullets to fragment (although they will still invert in the first few inches of soft tissue).
This is why Army doctrine as taught at OCS, OBC, and MCCC includes the lessons on Machine Gun Theory frankly states "30 Caliber machine guns remain the most casualty producing weapons as evidenced by after action reports from Mogadishu." I've had to take that particular machine gun theory class three times now, so it has stuck with me.
Bottom line, 308 kills things just as dead as 223 and much more consistently out to the maximum effective range of the weapon systems. Weapons in 5.56 can engage targets at 600 meters, but lethality in terms of getting an enemy out of the fight is lacking. Hence dusting off the M14s in Iraq and Afghanistan.
To sum up, I will quote Froggy....
Fr. Frog's Rules of Terminal Ballistics
1) There ain't no magic bullets!
2) Only center hits count
3) Make the biggest diameter hole you can to let blood out, air in, and destroy as much stuff as you can with each hit
4) Small bullets may expand, but big bullets never shrink.
5) Make the deepest hole you can to insure that vital organs and nerve centers can be reached and destroyed from all impact angles.
6) "Service" your threat until it is no longer a threat.
7) No small arm can guarantee 100% instant incapacitation of a determined adversary--man or beast.
8) Don't believe manufacturer's claims.
9) Inconsequential increments are meaningless.
10) Most gun writers are pathological liars.