The more I read and remember, the more I think we ought to reactivate the M-14.
One dirty little secret. The M-16 was adopted over the M-14, not so much for the reasons reported, but for the main reason that in the mid-60s, we had ceased being a "Nation of Riflemen" and the kiddies drafted from the big cities couldn't handle the recoil (kick) of the M-14 and were boloing on the range. The M-16, nothing but a .22 Long Rifle on steroids, didn't kick the kiddies so much and they were qualifying with it...but not becoming riflemen.
End of rant.
The BAR ( really a WWI weapon !) was good at the same range,and an excellent "light" machine gun : heavy and awkward to carry, but a LOT lighter than the air-cooled .30 machine gun.
One person in each 4 man fire team carried a BAR ( for some reason, it was generally the smallest member of the team. )
During the Korean war, a lot of the shooting was at longer ranges. People who were there said the 7.62 Russian rounds would "fall short" at those ranges, but the Garand and the BAR - in capable hands - would make life interesting for the Koreans and Chinese.
The single biggest determining factor in ditching the M-14 was that it was ungodly expensive to manufacture. Far and away one of the most expensive combat rifles ever produced by any country. The M-16 was something like half the cost per unit (and more accurate off-the-rack, not that it matters).
As for the ballistics of the .223, your are badly mistaken. If you've ever looked at physical models of terminal ballistics, there is a crossover velocity (2500-2700 fps, depending on the bullet) where terminal lethality takes on a new dimension due to reaching critical rotational energy densities. The .22LR has the terminal ballistics of a pistol bullet. The .308 sits on the edge of this envelope at the muzzle. The .223 is in it for about 100-200 yards out of an M16. I've never met an operator that wasn't quite pleased with the performance of the .223 when it mattered and even many old-timers prefer it.
And for those interested, the critical rotational energy density has to do with fragmentation behavior. Below the critical threshold, fragmentation adds little or no value to the terminal characteristics of a bullet. Above the critical threshold, the energy density is so high that the bullet literally explodes quite violently with the fragments travelling perpendicular to the center axis of the bullet at velocities around 250-300 fps depending on the specifics as a simple consequence of physics. At those velocities, bullet fragments are quite capable of perforating tissue, particularly in distressed tissue (like a temporary cavity). Hence why a good hit at relatively close range with a .223 can turn the insides of a person into hamburger that substantially exceeds the expected damage. The tumbling bullet causing damage bit is something of a myth -- ALL bullets tumble when they hit tissue. When it happens to bullets that exceed the critical rotational energy density, this frequently triggers the very energetic radial fragmentation.
And no this was not a design consideration when the .223 was originally selected. It was a fortunate coincidence.