That wasn't really the rationale behind the M-1 Carbine; rather around 1939-40 or so, while studying German blitzkrieg tactics, the Army realized that rear-area support types traditionally not armed with rifles because of the nature of their duties could suddenly find themselves in a firefight with enemy troops and needed something better than a pistol to protect themselves, and decided as a sort of light compact rifle firing a sort of hopped up pistol round. It was also realized that the weapon could also be used by front-line troops who might not normally carry rifles, such as officers, weapons crews, & radio operators.
The winning proposal was a Winchester design that combined elements of the actions of the M-1 Garand & the Winchester Model 1905 rifle, and used a cartridge derived from a commercially unsuccessful .32 round developed for the 1905 rifle, which proved unfortunately underpowered (military loads have the about the same stopping power as a .38 Special, itself considered marginal as a pistol cartridge). The carbine, because of its light weight and large capacity was often misused as an infantry rifle, and the poor stopping power of the round (stories from the Pacific in WW2 & Korea of soldiers emptying a magazine into a charging enemy solider without stopping him) combined with the fact that even light cover or vegetation would stop or deflect the round (i.e. the complaints against the 5.56mm of the M-16/M-4 magnified), led to much of the M-1 Carbine's poor reputation, exacerbated by rather uneven quality control.
The idea of such a weapon being seriously considered by a military, as others have stated, would probably require WW1 infantry combat being radically different than OTL, with a lot of close-quarters fighting, as there probably wouldn't be much of a civilian market for such a weapon to justify the costs- too small of a cartridge to make a hunting rifle, a .22 would be adequate for pliking 'varmints', & and the people who might want a lot of close-quarters firepower would likely go for a SMG, and otherwise, the concept would be too radical for the military.
If there were greater budgets for small-arms & ammo R&D and procurement in the interwar era (including a willingness to dispose of a lot of WW1 surplus stocks which were tiding the world's militaries over in that era), as well as military establishments more likely to take risks, which in itself would likely require notable changes to economic & political factors there might be semi-auto weapons along the lines of a M-14 or an SKS with a high-capacity magazine firing cartridges such as .276 Pedersen, the .276 round the British experimented with and planned to adopt before WW1, or a version of 7.62x39 Soviet developed earlier as standard infantry weapons in WW2.
About the only weapon that might change thinking that I'm aware of is the automatic rifle developed by Federov, which used Japanese 6.5mm Arisaka rounds with a reduced load. From what I've heard, the few thousand that were around were liked in the Russian Civil War, but were plagued with reliability issues that weren't resolved due to the disruption of R&D and manufacturing. A POD that causes that weapon to be more widespread, well-known, well-liked by users, and debugged might provide an example, although it would still but up against traditional notions of proper rifle marksmanship and cartridges in the military establishments, as well as budgetary & political constraints.