The US had the similar .30 Carbine (7.62x33) at about the same time the Germans had the 7.92x33 Kurz and made about 5 million of them during WWII.
The M-14 was an attempt to reduce the .45, .30 Carbine and .30/06 rounds and M-3 submachine gun, M-2 Carbine and M-1 Garand and BAR to a single weapon and ammunition. A laudable goal, but it took the acceptance of smaller caliber M193 rounds to make it moderately practical, with all the limitations, and even now squads get a different machine gun, and the M-16(A4) is supplemented with the M-4.
A controllable LMG with a full power round is possible, and the Chauchat in 8mm lebel did it in WWI. You wouldn’t want a long recoil system in a rifle, as it could be pushed out of battery in close combat. Chauchat had problems, but control wasn’t one.
If I was king, I would have a 5.56mmX45 bullpup weapon with a quick change barrel, so a heavy barrel could be dropped in to get a light machine gun capability, or a lighter barrel could be dropped in for a more mobile rifle. I also prefer delayed blowback to gas operations mechanisms. Note: patent 6,079,138 is over 10 years old.