@McPherson, are you trying to argue for a universal cartridge (ala 7.62 nato) or common caliber (such as the soviets use of 7.62 tokarev and 7.62*54R)?
Yes and no.
Look; there is a realistic physical limitation to the size of a bullet, the mass of a bullet and the propellant loading one can pack into a shell casing to shove that bullet. There are [also] numerous subtle aerodynamic influences that affect bullet performance in a weapon. Take for example the US 30-06 bullet. It was/is a 9.7gr to 11.3gr bullet of 7.62x63 mm either of a flat tail or boat-tail configuration. This bullet was derived from the round nosed 30-03, which in turn was derived from the 30-40 KJ rifle round the US army used in the Spanish American War.
Summary: the US discovered after WWI combat that the Spitzer bullet it thought it used in the Springfield rifle and in its machine guns did not have the 4,200 meter flyout range the Army Ordnance people who "tested" it claimed. Flyout was about 3,000 meters. The British, French and the Germans, who had ~4,000 meter flyouts had tested their bullets to use "beaten zone" machine gun tactics or indirect harassment bullet hose fires to get behind the trenches and cause casualties behind the presumed safety of the front lines. (Trust me, it is cheaper than mortar shells and it is effective to keep people miserable and or under some cover, hence communication trenches reaching at least a 1-2 km back.).
After getting their act together, the Americans improved the Ogive on their bullet (i.e. copied the Mauser bullet as well as the rifle.) and improved the aerodynamics to achieve a comparable performance of 4,000 meters or more.
Then there was the problem of Mister Machine Gun. Not only did the propellant in a bullet need to shove the bullet, but a bit of that chemical energy is also used to drive the machine gun. Whether gas tapped to operate a drive rod, or direct impingement to drive a bolt; the indexers, cams and ejectors drew off up to 50% of the propellant energy (depending on the principle and the type of machine gun), packed into each shoved bullet's propellant case. There is a decided difference between a rifle round propellant load and a machine gun round propellant load. Get the two confused in WWI and WWII, and the result could be a uncontrollable muzzle rise and/or rifleman with a badly bruised shoulder; or a hang-fired machine gun with a feed jam due to failure to extract. Messy and downright inconvenient on the firing range, it is fatal in combat.
The obvious solution is to design the (bolt action or straight pull) rifle to dump gas at the muzzle; so as to down rate the TIME the shove forces have and to mitigate recoil (short barrel). Or to design a rifle bullet and shell casing that is idiot proofed to the rifle and unusable to the machine gun and vice versa, or develop a self loader rifle that uses about the same amount of work to drive its cyclic as the machine gun. (An example would be the Johnson self loader battle rifle and light machine gun.).
Throw in the carbine and try that with the same bullet/shell casing propellant mixes? Now you have to dump gas AND have to use a self loading system so your carbine is short barreled and a full or semi-auto weapon. (and probably uses a muzzle brake to help with climb and recoil).
Have I mentioned rifling? (^^^) To get enough rotations out of your bullet to keep it stable at muzzle velocities of 600 m/s to 800 m/s for the carbine the twist is about 1.25 in (I'm estimating here) 40 centimeters of barrel length. Congratulations; your carbine has to have a barrel length of 15 inches at least as they measured in those days. Guess you better start thinking about BULLPUPS for your paratroopers.
The tradeoffs you have to make for a universal bullet are incredibly complex. No wonder the British, once they have the Vickers machine gun and the Enfield in the .303 common, are NOT going to monkey around with a new battle rifle. The US screwed around with the M1 Garand for a full decade and likewise with the Browning .30 machine gun and finally solved both about 1938. I think the .30 Browning still used "machine gun ammunition" but the 30-06 rifle rounds that passed through it would not hang it up. As for the Germans... MG 34, 42, K-98 and the FG-42 ALL used the Mauser cartridge with various degrees of success. (The FG 42 was a shoulder bruiser and a muzzle climber, until heavily modified.)
This also explains why you use gunsmiths and NOT automakers, or government weapon testers to reverse engineer a piece of enemy kit you like. GM is bound to screw up any piece of ordnance you give them. HS404 or MG 42, or FG 42.
Might also say the same about US Army Ordnance.
Clear [operator] head space is no joke. (cough "M60 machine gun" cough].
McP.