Small arms are a side show for most large militaries. Bombs with their delivery systems, ships, aircraft, artillery shells, rockets, missiles, etc. instruments of mass mayhem are the big ticket items, even during the 1920's-1960's.
In bad budget years such as during the 1920's-30's, the urge to move to a new caliber firearm that would require either A) having two separate cartridges, a .276 Pederson and a .30-06 as the machine guns were in .30-06 such as the light machine guns, the BAR, etc. would complicate logistics, manufacturing (Frankford and contractors would have to operate two separate bullet lines), and so on.
The Brits were similarly constrained as were the Germans, Russians, and to some extent the French. The professionals in armies weren't dummies that failed to recognize the potential of new cartridges, but the marginal improvements at fairly large budget, training and logistics complications, made a cost/benefit analysis that the status quo was good enough. So a lot of the pre WWII efforts were made in streamlining production with marginal improvements in perceived deficiencies (the no. 4 series with good peep sights and easier to manufacture, the French aborted move to the newer MAS 36 with the transition to the MAS auto firing series in mind, the US move to the Garand semi-auto, the Germans settled on the shorter 98k, open sights with settings down to 100 m, and decentralized production, and the Japanese recognizing the limitations of the 6.5 Arisaka and attempting to move to the more authoritative 7.7).
Wartime rules are different and rulebooks get tossed in the imperative to improve military performance but then peace soon or later comes with diminished budgets. The Cold War era of planning the use of atomic theater weapons in Central Europe to combat the mass Warsaw Pact hordes made the whole 7.62 NATO debates rather an academic sideshow during the 1950's. The move to magazine fired weapons and a new generation of machine guns was quite enough for Pentagon procurement folks that were much more concerned with air superiority, the development of missiles, nuclear artillery shells, new tanks, etc. along with the training, procurement,and logistics of moving from the .30-06 to the 7.62. Realistically, the Americans, aside from NIMBY, was not going to move to the British newer 7mm based round as the British themselves could barely afford to re-equip its military with the ancillary light machine guns,etc. The British also borrowed heavily from the US during WWII's earlier stages to equip its forces and provide food to the populace. Due to Uncle Sam picking up the assorted bills for NATO along with offering trade concessions to keep the West united, it could afford to call the tune to its liking.
It liked the 7.62 NATO as good enough, the M-14 as a budget cutting do all, and the new NATO round being a quite good substitute for the light machine guns to replace the older outdated WWI era machine guns.
If you recognize the well-being of individual troops/sailors/Marines/airman are not the primary concern of the bureaucracy in the Pentagon except when forced on its attention during wartime due to casualties and the ensuing public pressure to fix it, then you can understand how the defense bureaucracies in the World continually make decisions that result in casualties down the road. Other things are simply more important to them. It is a perpetual defect in bureaucracy that the more remote the leaders at the top from accountability and direct consequences of their actions, the worse it is for the poor sods at the bottom of the pyramid.
As the old saying goes, if you ain't the lead dog in a sled team, the scenery never changes.
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