The "wound not kill" design parameters don't come into effect until 5.56mm NATO and the corresponding USSR rounds were introduced in the late sixties/seventies.
This is also a myth, invented in retrospect to explain the poor performance.
The original 5.56mm was actually very much a killer round. To remind, it was 55 grain back then, and it was fired out of a barrel with 1:14 twist in Stoner's prototype. This made it understabilized, which would cause it to yaw and fragment very consistently in tissue, causing extreme permanent cavity sizes, and fist-sized exit wounds on human targets. In combination with burst fire (and to remind, the entire 5.56 thing was a sidetrack of Project SALVO, which was all about making a weapon that could fire controllable, accurate bursts.
But understabilization negatively impacts accuracy, and US army brass still clung to their notion of accurate rifle from the trenches, so they asked the twist to be increased to 1:12. This still worked reasonably well with a 55gr round out of a 20" barrel, though less so than the original. Then, finally, some idiot decided that a rifle round should reliably penetrate the standard-issue helmet at range, and so the steel-cored SS109/M855 with its 1:7 twist was adopted as a standard round - and while it does indeed penetrate really nicely, it doesn't tumble nor fragment reliably at any range. Then USMC fucked it up even further by coming up with M16A2 which replaced full auto by the useless three-round burst, and generally shying away from the concept of automatic fire by riflemen and pushing their "one shot, one kill" thing; Army actually objected to many of the changes, but they were forced to adopt M16A2 as well due to budgeting reasons.