True.. But I suspect if the UK / commonwealth already had a rimless .303 round there would have been a distinct lack of enthusiasm for replacing that round with the historical 7.62 x 51. I do agree that the UK / commonwealth would have likely been more enthused about adopting a lower power round.The justification was that the British Army had teams of statisticians surveying battlefields and interviewing combatants during WW2. They knew they needed to replace the bolt action Enfield with a SLR of some description. The statisticians established that most combat occurred at circa 300 yards with an upper limit of 500, the 303 was massively overpowered for combat at those ranges so the Army started looking at self-loading rifles in the 6.5-7mm range though some of the prototypes used 7.92 Kurz (mainly as it was readily available) one justification was it would allow troops to carry more ammo, could be used in full auto if necessary due to low recoil, was shorter than an Enfield and . What they eventually settled on was a the EM2 also known as Rifle No9 Mk1 which was smaller, lighter and shorter than a SMLE.
The US forced the whole 7.62 NATO thing as they didn't want a "light" bullet as only a manly 30 calibre bullet is good enough. Ironically within 5 years 5.56 was a thing.
All that being said perhaps politics would have resulted in the UK / Commonwealth adopting what ever the U.S. wanted.