There is one school of thought that blames the 5.56 (and the 9mm) on the USAF. As one wag put it, General Lemay wanted his nuclear bombers guarded with something more modern than M1 Carbines, and the AR15 was space age enough to suit him. Of course the Army would not be outdone and bought the same.
That's one way to look at it. I don't think its fully correct, but it is a way to look at it.
In the version I heard, its still Lemay that's responsible, (and only for the 5.56mm, not the 9mm) but not because he wanted something "more modern". It was because he didn't have any other choice.
The Army was phasing out the M1 carbine. The Air Force got its small arms, and their support (spare parts) from the Army. With support for the carbine going away, Lemay had to find something else. He was introduced to the AR (and Stoner) and thought it would be a good gun for his airbase SP's (who, after all, don't normally get down in the mud like regular infantry).
A bit later, the MacNarama Defense Dept (whiz kids) decided that the AR & 5.56mm were the best for EVERYONE, and pushed them through as a "fully developed" weapon system, needing no further work.
Bugs/flaws did show up. Some of them were even possibly deliberately caused by those more interested in discrediting the weapon than in saving US blood. So sad.
The powers that be were determined to make the AR & 5.56mm work. Took decades to get the real flaws resolved, but they finally did it. (aside from the argument that the real flaw is the 5.56 caliber).
I believe that had the M14 been retained (in part, anyway) and given the same tinkering with, it would have wound up a much better rifle than it was when it was mothballed.
I do recall hearing about some guys who did some experimenting with the M14 gas system, reducing the cyclic rate with what was supposedly a fairly simple modification, and finding (guess what?) at a lower cyclic rate, the M14 is "controllable" in full auto fire. As far as I know, the military never even looked at that possibility.
Politics.