The Germans did that study in 1918. The US actually did theirs during Korea, so later than the Brits. The SCHV round actually came out of a side project with the M2 Carbine:
https://www.amazon.com/Black-Rifle-Retrospective-Modern-Military/dp/0889351155
The value of the AR-15 was only recognized later; originally it was adopted by the Air Force to guard bases and only adopted by the Army because of the M14 being too much gun for the mission. The M16 then was the only option, as it was the only other rifle available in numbers:
https://en.wikipedia.org/wiki/M16_rifle#Adoption
1. Actually, the first US study of a 22 caliber SCHV dates back to 1895 in the .22 Krag, there was also another study (possibly more than 1, I don't have access to the second) seriously comparing the .220 Swift to the .30-06 which showed several things like the fact the Swift had superior penetration against steel than the .30-06 among other things. (the .220 Swift at the time absolutely destroyed barrels of the era however, it even does today unless you don't cheap out on a good barrel.)
Also, the fact they did it before and during Korea sort of goes with the "post war" thing, as that would infact be directly after WW2, the point was just because the British did their own study, people think the US didn't and somehow the British had all this wisdom from the war the US didn't which doesn't fit the narrative.
The M16 was selected not because the M14 was "too much gun", but because it was actually horrid, there was the option of going back to the M1, maybe the FAL (if that door was even still open.). Also, the M16 wasn't even intended to originally stay in service, it was intended as a stop gap until one of the SPIW platforms was put into service which although also .22 caliber, fired all kinds of oddities from Duplex loadings to Saboted Dart loads.
The SPIW program was ultimately cancelled however, and it turned out the M16 was not only just fine as a front line combat weapon, but that it would revolutionize the future of front line weaponry everywhere.
This is why you don't quote Wikipedia in a debate.
Given that the M16 was only given a chance by the army because the M14 was just so patently overpowered for the role and unsuitable for full auto fire, if the Pedersen is more manageable the army may well never give the M16 a chance.
In terms of the 7.62, the Russians never dropped it, they have supplemented heavily with 762 based weapons (including AK-47s especially for urban fighting), as the 5.45 round is fine for some roles, but is just not a big enough bullet for many other roles. As it is the Russians apparently are even trying to adopt the 6.5mm Grendel round now or even neck down the 7.62 to a 6.5mm bullet (the Grendel-ski as it has been nicknamed) as a replacement. Apparently the Serbs even adopted the Grendel for their Special Operations forces, while our own have used things like the 6.8mm SPC.
https://en.wikipedia.org/wiki/6.8mm_Remington_SPC#Military.2Flaw_enforcement_adoption
It was given "a chance" because the Army was investigated and found to be rigging tests in the M14's favor, and that whole thing about it because a garbage bin of a rifle that should've lost to the FAL. the Pedersen had nothing to do with this, even if you chambered the M14 in it, it would still be a painfully mediocre rifle and that wouldn't solve one issue that's being missed here, that Intermediate =/= SCHV.
SCHV focuses on high speed, small rounds for various reasons like good trajectory, low weight, very little recoil, etc etc etc. This is inherently different from previous "intermediate" rifles like the STG-44 (Unloaded Weight: 11lbs/5kg, Ammo Weight, 17 grams a round) the AK-47 (Unloaded Weight: 8lbs, ammo weight 17.2 grams a round.) the EM-2 (Weight: 8lbs: Ammo weight (.280): 20.5 grams, the .276 Pedersen would be closest to this in weight and likely recoil as it weighed 19.3 grams).
M16....7lbs, ammo weight, 11.50 grams M193 loading, 12 with almost all other loads with the exception of Mk 262 at 13 which is still significantly less, the SCHV concept also means that it has a much flatter trajectory than the above cartridges and much lower recoil for easier control and accurate follow up shots.
(The fact the AR-15 is is also a more mechanically accurate weapon than then M14, STG-44, AK-47 and EM-2 also tended to help alot.)
No, the Pedersen isn't going to somehow cancel the adoption of a .22 Caliber cartridge, because even if it's not 5.56x45mm (which is really unlikely as both the cartridge and the weapon aced the CONARC requirements), it could be 5.6x53mm of the SPIW or many other .22 caliber cartridges the US was looking at,
Secondly, The Russian Military did in fact drop 7.62x39mm, some police units still use it, some SF units still use it (allegedly because there's a load of Subsonic rounds and weapons left for it, but aside from the Russian SF, NO ONE knows for sure why the Russian SF uses it.) there's no supplementation with 7.62x39mm at all, and as any ballistician knows, I'm sorry to tell you butr bullet size is not every thing, not by a long shot. 5.45x39mm is just as, if not more lethal than 7.62x39mm while offering all the benefits of the SCHV concept.
Thrid, this isn't even the 1st time the USSR/Russia has experimented with a 6.5mm cartridge, the first time they did, they were less than impressed with it, the fact this has gone nowhere says history is repeating itself.
Lastly, no, that is completely fabricated By Chris Murray's and Gary Robert's (probably the 2 biggest faces of the 6.8 Mafia, one a complete psychopath and the other a pathological liar, great team) mass disinformation campaign, what Babby said is 100% true, the closest the US has ever come to actually using 6.8x43mm SPC is having a test team trial a few rifles chambered in it, they all broke, that was the entire and very brief history of the US Military's consideration for the 6.8x43mm SPC.