Actually, I recall that one of the US's most successful snipers used an M2 in the Vietnam war. https://en.wikipedia.org/wiki/M2_Browning#M2_as_a_sniper_rifle
Are there any reasons weapon manufacturers settled on 7.62 and 5.56 for bullets?
Do those sizes have any particularly good aerodynamic qualities that, say, 6.32 wouldn't have?
I'm surprised nobody has apparently mentioned the AK-74. It uses a 5.45x39mm round and was adopted during the 70s to rival the M16. But they didn't become as popular. There were an estimated 100 million Ak-47s produced but only 5 million Ak-74s.
The difference between an AK-47's round and an AK-74's isn't quite as profound as that between an M-14's or G3's 7.62x51mm and an M4's or SA80's 5.56x45mm. The 7.62x39mm was already a lighter, less powerful, easier to control round for automatic weapons than the Russian/Soviet rifle round, the 7.62x54mm. The 5.56 weighs less than half (11.8 grams) what a a 7.62 NATO (25.5 grams) round does. A 5.45 (10.5 grams) only weighs a third less than a 7.62x39mm (16.3 grams.) As well established and widespread as the AK-47 (and SKS before it) was when the 5.45 was introduced, there was far less impetus to make the switch.
I read someone recently who was talking about the newish 6.5mm Grendel round and answering the question of why didn't the US or NATO adopt that, since it's better than the 5.56. His explanation was that it may be better, with characteristics 5 or 10% better in all categories, but that wouldn't justify the vast expense of the changeover where many military organizations have a total of many millions of weapons already using the 5.56. It's just too big of a cost for 5-10% improvement in performance.
Abstract
Operations in Afghanistan frequently require United States ground forces to engage and destroy the enemy at ranges beyond 300 meters. While the infantryman is ideally suited for combat in Afghanistan, his current weapons, doctrine, and marksmanship training do not provide a precise, lethal fire capability to 500 meters and are therefore inappropriate. Comments from returning soldiers reveal that about fifty percent of engagements occur past 300 meters. Current equipment, training, and doctrine are optimized for engagements under 300 meters and on level terrain. This monograph reviews the small arms capability of the infantry squad from World War I to present. It then discusses current shortfalls with cartridge lethality, weapons and optics configurations, the squad designated marksman concept and finally the rifle qualification course. Potential solutions in each of these areas are discussed.
http://www.thedonovan.com/archives/2010/03/taking_back_the.html