Well, it happened first in Japan. They made an anemic little round- actually, probably about ideal for antipersonnel use- 6.5x50mm, I think? This was before 1900. The Russians made the first "assault rifles" for this cartridge before 1920.
You might appreciate those sissy little rounds if using them instead of big manrounds meant you had double the ammo, and didn't have to run out of fodder to make your rifle go bang, as happened at various battles in the Civil War, and to the defenders at the Alamo.
See, the big advantage of using a smaller round is LOGISTICAL. The reason the COMMON SENSE SOLUTION of using a smaller round was not a significant disadvantage, was that engagements typically occur well within the power envelope of the intermediate cartrige. Longer ranging fire is handled by support weapons.
The "sissy little" .223 is a different approach than the 7.62x39mm. The Russians were frantically trying to keep up with German small arms advances. They already had a .311 diameter cartridge, so making an intermediate cartridge in the same caliber just simplified things (which is what the Germans did as well). The US had the luxury of time, and made the decision to go with a smaller diameter, faster round. This smaller, faster round meant about a 50% increase in useful range over the manly, large diameter 7.62x39mm. Terminal effects were just an additional bonus.
The sissy little .223 underwhelmed the Russians so much, they took their parent cartridge for the AK, and necked it down so it could be sissy, too.
Now, again, the obvious solution, is for the US to find a cartridge that is significantly smaller and lighter than the 7.62x51mm, yet heavier and more powerful than the 5.56x45mm. This will enable a single cartridge to replace BOTH ammunition types. A 6mm bullet at about 3000 fps should be close to ideal, giving a round with range comparable to a .308, but with recoil and size closer to a .223.
Just curious- what defines a "big bore" to you? The Garand was originally a .276, and probably would have been a better rifle for it.
John