If SOCOM wants a new battle rifle in 7.62 they get it - and did - the FN SCAR. While no longer buying any more of them, I don't believe they "sold them off" and remain in the racks for use when needed.
Same with pistols - if they have an op that requires some deniability they buy and use Glocks. Obviously Big Army did not. So it goes, if they perceive an issue might be solved with an alternative round, then they look for an answer and participate in it's development or just buy it off the shelf.
Nobody anticipated 6.8 SPC, it never became an US official round, yet there it is, 100% SF and AMU designed and used. I would not expect it to replace 7.62 as a machine gun round in Big Army any more than the lightweight 6.5's. When you move into crew served weapons the requirements for anti material become more important - and 7.62 comes in armor piercing, gets mounted on vehicles, and can be used at 800m+. The general infantryman isn't even trained or kept up in skills to do that - only dedicated long distance shooters get that role and they are few and far between. Normally a few in the Battalion assigned to specific missions as a surgical tool, not the hundreds humping guns on security patrols.
There is a reason for inertia in Big Army and why they don't keep flipping cartridges and weapons for the latest greatest. It takes time to field them and then train the shooters. The more you have using the system the longer it takes. There are tens of thousands of MG's as organic weapons, and 90% are NOT in combat units but all the command and service support. The incremental advantages of one cartridge over another when used in the defense simply don't materialize on a day to day basis. It's the single sniper team specifically and technically held to a high skill level who take advantage of it.
For the most part MG teams are shooting at opponents with the same level of weaponry - or less - a bullet with 25 grains more weight in armor piercing and tracer will deliver more impact and direct fire better than the lastest SOCOM sniper rifle of the month. We give the special unit soldiers a bigger plate to handle, they need the tailored weapons and rounds, but by no means are we going to switch over wholesale to those just because. They don't get Eggs Benedict in the chow line and I wouldn't expect the rank and file to get them either. It's the civilian who has an overfocused interest in exotic superweapons who create the demand to have something just like it and they push for having them for the presumed "superior" ability - to enhance their status collecting Operator Chic.
If it's a bid under SOCOM its usually something that will never go Big Army. Whatever it is they are looking at will remain a niche item. When Big Army hands them something to test as part of development, it's usually early on and often we never hear about it when it's asked "What did this do better?" In one specific case, we did - and the shooters across the board said the SCAR was cool and all, but it didn't launch bullets out the muzzle with any usable increase in lethality. If anything it was another gun to learn how to shoot under stress and that in and of itself wasn't a plus. Nothing game changing there, so SOCOM shelved it.
We could very well be discussing this as a footnote in 5 years, "Yeah they tried 6.5/260 but -"