Millions of carbine rounds means a direct reduction of 9mm and 303 rounds that are being shipped to the Front
As a practical matter of logistics, the drive to find a common round for pistol, carbine, rifle and machine gun is desirable.
As a practical matter of effect, the four classes of weapon are somewhat mutually exclusive as to servicing a common target set; the enemy soldier and enemy soft skinned vehicle.
I think one "might" be able to get it down to two rounds. Round nosed, low velocity, high mass bullet for pistols and close combat (under 100 meters) bullet sprayers (SMGS)
and one "type" Spitzer bullet for a "carbine", rifle and machine gun.
Difference in the Spitzer would be the propellant load. Some nations did this anyway to put more energy (chemical potential energy in machine gun ammunition to operate the "machine cycle" in the machine gun, for example.), so one could see three different shell cases for carbine, rifle and machine gun.
But that is 4 lines of ammunition again. Murphy.
'Cause I think a carbine should have been effective to battle ranges, which for an average human being is about 3 futbol (soccer) pitches in length.
By that metric, I think the M1 carbine fails the gerbil test. I don't think it would have been sensible for the British to mass arm with it. In any way, it was a miracle the Americans got what they did.
Look at this junk;
Is there a single one of those bodges, one would trust in the hands of Joe Infantry?