The .223 fails as both a big game and as a military round, despite having been used with some success in both roles.
The reason it fails as a big game round is because the hunter must accept that his round will produce a humane kill only if he avoids frontal and quartering shots. I will grudgingly admit that the TSX and other mono-metal bullets have changed the rules, but for shots that require deep penetration, the jury is still out. Headshots are tricky and seldom called for in hunting scenarios, and when they fail, they fail badly.
We all know that the .223 has been used as the primary combat rifle cartridge in Western countries since the mid '60s. Yes, a soldier can carry more rounds of 5.56 per weight than 7.62, but since its adoption, the number of rounds required to kill a single enemy combatant has increased dramatically; thus it appears that if you are armed with a .223, you will need that extra ammo. There are those who will argue that this is a result of the soldier having the ability to use full auto fire, but I believe that is only part of the story. As a rule, the bad guys don't want to get killed so they hide behind cover they hope will stop a bullet. When shooting at someone who is not in the open, and the bullet must defeat intervening obstacles such as brick and mortar, concrete, wood, glass, or sheet metal, the .22 is at a disadvantage compared to what we have come to recognize as major calibers. If we consider the big picture though, 80% of combat fatalities are the result of large weapons: missiles, rockets, bombs, artillery, etc, and while I don't believe that this makes the rifle cartridge irrelevant, from the war planner's point of view it is a place where he might be tempted to save money. A soldier can be trained more quickly on a .223 based weapon system, the .223 weapons systems allow a single type of weapon to be used for a greater number of roles (main battle rifle, submachine gun, squad automatic rifle, sniper rifle etc) which previously required different firearms chambered for different cartridges and created a logistical problem. But if the problem is to simply choose a round that will take an enemy out of action with a single center torso hit, any of the full powered rounds from 6.5 to 8mm are better than the poodle shooter.