I’d probably prefer keeping it an “alliance vs alliance” setting in terms of factions, rather than turn ‘NATO’ into just the U.S. Army or something. This is purely for flexibility and convenience sake. For example if we want to visit other places of the earth or undertake specific operations. But ofc I’m totally fine with the actual unit itself being fully US under the NATO flag. Considering we pretty much unified all nation’s armies under single flags anyways
My humble suggestion
Taking inspiration from an old TTRPG called "Twilight 2000", I think it'd be cool if we could deepen NATO's lore a bit to match the current situation they're in.
My suggestion is that NATO as we knew it before and during the war no longer functions, and what we see now is a morbid shambolic parody of international co-operation. With so many European governments either overrun, dead, or puppeteered by either the Soviets or the Americans, the US government, now decidedly more war-hawky and authoritarian thanks to years of war, decided to do away with the notion of an internationally led alliance and effectively "couped" NATO, not that there was anyone willing or able to resist them. European troops were pulled away from their home continent without their permission or consent, sent to the good ol' US of A to defend it from an upcoming Soviet invasion. The faction is still "Multinational" and called NATO in name, however it's fully under the thumb of the US military, led, supplied and wholly at their whim. Everyone answers to the US President now, or maybe if they're lucky, some sniveling fat-cat puppet who answers to the President in turn.
NATO's been losing the war, for a very long time now, and if it's to the point where Soviet troops practically occupy all of Europe (has ingerland fallen? Does the hammer and sickle fly over the chippy?), and now in the US, they'd be in an extremely desperate situation. It'd be nice if their lore could reflect that. It'd also give NATO some character and internal conflict beyond "We are the happy diverse coalition of good guys here to fight the bad guys". It'd also make more sense to have a US-led unit with NATO troops press-ganged into defending the mainland US than it would to have an epic top tier multinational reaction force in the US. (One imagines those sorts of units are probably wiped out by now if the Soviets are doing this well).
In short:
To show the effects of the war on the alliance and how desperate they're getting.
