I think the .223 is lacking as a big game round, but that doesn't seem to prevent lots of people from harvesting big game with them.
IMHO, for a cartridge to be considered for big game it must have a resonable expectation of killing the game animal with a single shot from any angle within the range limitation of the cartridge. If you have to make excuses like, "it must be a broadside shot," or "you must surgically place the bullet," or if you assume you must fire multiple shots to bring the animal down, then I believe that either the bullet or the cartridge is is unsuitable.
Barnes now makes a .224" TSX, so once again the rules of ballistic performance will change thanks to Randy Brooks. He keeps this up and I'll have to swap my .375 Ultra for a Mini-14. Even so, again IMHO, big game cartridges start at 6.5.