My dad carried a BAR in WWII and said the BAR's weight made fair accuracy with short bursts possible. He preferred the BAR models with semi-auto/full auto switch over the newer ones with the slow rate/fast rate switch. But he said even the slow rate would allow you to tap off one or two shots and stay on target. Even though the BAR fired from an open bolt, it had a long barrel and a ladder type rear sight that allowed hitting individual targets at fairly long range (way over 200 yards).
M14/M15 was definitely too light for full auto even in 7.62 x51. I remember the hoopla about the New M14 wonder rifle replacing the M1 Garand, the Thompson, the M3 grease gun, the M1 and M2 Carbines, the 1911A1 pistol, and presumably the trench style shotgun. M14 is a nice semiauto battle rifle, but man was it oversold.
I remember the THE SAND PEBBLES, saw it as a kid on its theatrical run. Great movie, and it starred the guy who saved the world from THE BLOB.