The Carbine was designed and intended for rear echelon troops, clerks, cooks, and truck drivers. The Garand was deemed too large and heavy for that purpose.
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Just about everything you said is mistaken.
The Army's Chiefs of Infantry and Artillery recommended development of a light rifle in June 1940. The SecWar accepted this recommendation.
The 1 October 1940 T/O for an infantry battalion (the last version before adoption of the carbine) called for 601 Garands and 313 pistols. The next edition, 1 April 1942, had only 60 pistols and 469 Garands - but 290 carbines. So, actually, the carbine replaced about 80% of the pistols and 20% of the Garands - not in rear echelon units, but in the very core of combat units. In WWII combat and combat support unit T/Os, it is very hard to find any cook or clerk authorized anything other than a Garand until you get to units like field artillery or chemical mortar that were 95%+ carbines.
Even higher up the chain, the infantry regiment service company - the closest administrative formation to the front - had over twice as many Garands as carbines (including Garands for all 14 clerks plus all 3 cooks and 25 truck drivers).
Yeah, I know. Qualifued X-spurt with it in 1957. MOS was ammo truck driver for Service Battery of 105 SP’s.