As I recall, one of the primary motivations for switching to 5.56 NATO was that you could carry roughly twice as much for the same weight as you could 7.62 NATO.

Absolutely correct, this has been understood since the logistical demands on German troops in WW2 required 8mm Mauser rifle rounds meant that they needed constant re-supply for more ammunition. Particularly the MG-42's that made a Machine Gun team over 6 people IIRC.

Full-on 7.62 NATO battle rifles are also very hard on the troops using them, I've heard them described as "fully-automatic flashbangs", with deleterious effects on situational awareness due to the power of the round.

That's kind of what you get when the idea of a squad automatic weapon is a BAR... which is supposed to be fired from the hip, and comes with a bipod. It's really more of an LMG, but when it was invented intermediate cartridges didn't really exist. It's an improvement on what was already in front of them, but it's not necessarily a great idea.

That being said, the sound of a bunch of 7.62 weapons firing on your position with automatic fire is going to be absolutely pants-shittingly terrifying. The sound of a platoon normally firing with 7.62 is cacophonous. There's no way that the sound doesn't have a significant effect on enemy morale.

The next calibre the US is after is 6.8mm. Not that I expected them to actually choose a 7mm round, that would be a little too on the nose.

"Oi Mate, you got a locinse fo dat 7mm?"

"It's not a 7mm, it's a 6.8 mm"

"Swings an' roundabout's govenah."

"IT'S NOT A 7 MM"

"Aw thinks u might be compensatin' fo sometin' "

"IT'S NOT A 7 MM!!!!!!"