The main issue would be using diferent ammo for rifles and MG, which was not regarded as acceptable at the time. Virtually all WW2 era armies used the same ammo for their rifles and their MG ending up with overpowered rifles rather than underpowered machine guns. A few countries used heavier rounds for their heavy MG, keeping the rifle caliber LMG. The Swedish army even made a rifle for their heavy MG round, so that the HMG crews used only one type of ammo, ending up with a rifle that was too overpowered for infantry use.
The use of a different caliber for the carbine was tolerated because it was regarded as a new class of weapon, in fact a PDW meant to replace pistols and SMG.
Of course armies routinely supplied parts for a multitude of different equipment and managed to deliver the right parts to the right unit, but somehow ammo supply was regarded as something that had to be kept as simple as possible.