Sullivan’s comments about 5.56 lethality are absurdity that’s for certain. The 30-06 and 7.62 are unquestionably more lethal.
.223 is basically a hopped up varmint cartridge.
I don’t know how much truth there is to it, but have been told more than once that when you wound someone on the battlefield, it often takes a couple more soldiers out of the fight trying to save their wounded comrade. So a cartridge that would be nearly 100% fatal would not necessarily be such a huge advantage.