The rest of the factions are weirdly designed in my opinion and trying to forcefully be "different", as in the reason why we got both British Armies being focused around static defensive emplacement gameplay or both the PE and OKW being the "Elite" more vehicle focused factions.
What should have been done in my opinion was go for a theme and stick to it, for example I think it was well done in the original CoH with the US and Wehr representing their real life 1944 counterparts well while in this game the Ost is some sort of mish-mash 1943/1944 defensive Army while they should be an early war more mobile and aggressive Army with the OKW's trucks instead to represent the "Blitzkrieg" time of most of the Theater of War missions for example.
In CoH1 USF was early game Wermacht were late. It was usually up to the USF player to be offensive and attempt to shut out the game before it was too late. That was the "theme" of the game and I think plenty of people were fine with that.
I completely agree with you in that the base factions are not deprived but have "themes". CoH2 Soviets and Ostheer are pretty closely matched and commander choices allow you to decide what niche you end up wanting to fulfill. Such as Assault Grenadiers if you wanted early offensive power, or T85's if you wanted a heftier tank. Did Ostheer have a better late game? They did, but that doesn't mean Soviets couldn't compete.
In CoH2, USF were similarly designed around shutting out the game on a razors edge. They were on an invisible timer to lose the game. They lack units in their core army because Riflemen were designed to do everything. As you said when they removed smoke on rifles, this core design began compounding on itself until they turned into this weird faction we have now. We have units that constantly compete against itself or just "slight" variants of existing units.
as for OKW I think the idea was they were mimicking their "Battle of the Buldge" concept of striking hard and fast early on, then teetering out to retaliation, but if they COULD hold they finally get their big guns out, the ultimate late game if you will.
I protested a lot of the USF changes that turned into the current iteration we have today and I was not the only USF player to do so. I prefer the theme they were originally presented with, and instead of changing it would prefer reducing the impact of it. If the issue was "Well, USF didn't have a late game" that was a choice you made when you locked the faction. I'm not a fan of factions being slightly different flavors of ice cream.