Larry Ruth in "M1 Carbine: Design, Development and Production", The Gun Room Press, 1979, cites Major H.P. Smith and William H. Davis, "History of Small Arms Material U.S. Carbine, Caliber .30", Small Arms Branch, Industrial Division, Ordnance Department, 1945.
In a letter of March 25, 1938, from Rapp Bush, Lt Col, Infantry, Subject: Weapons and Ammunition carriers, to: The Chief of Ordnance, Lt Col Bush goes over the large number of personal who would ordinarily not be armed with the rifle but with the pistol, and the combat load of such personnel being close to what is humanly bearable, and ends with a specification:
The Chief of Infantry considers that the type of weapon required for ammunition carriers is one fullfilling the following general characteristics:
a. Weight (weapon and 20 rounds of ammunition)--not to exceed five pounds.
b. Range--Effective at 300 yards.
c. Magazine Fed.
d. Operation --Automatic desirable; semi-automatic essential.
e: Method of carrying--Over shoulder with sling.
To get the weight of a usable automatic rifle under five pounds they looked at the 1905 .32 WSL Winchester Self-Loading as a candidate cartidge. The .30 Carbine was developed from that older round before any carbines were designed.
The design goal was rifle+20 rounds at five pounds total (all the extra weight an ammunition carrier for .50 M2, 60mm or 81mm mortar, or 37mm antitank gun, could reasonably be expected to carry).
Nothing about must only wound enemy to tie up additional enemy personnel.
Added: wouldn't a .45 1911, web belt, holster, magazine pouch and three loaded magazines push that magic number of 5 pounds?