So the possibility, using the level of abstraction in HoI 4 -- and in just about every other war game on the strategic level -- and having 100% historical accuracy is slim to none. I've been playing WW II games from the level of high strategy like this one to squad level tactical varieties, and even one of individual soldiers and equipment with a single squad-sized unit, since I was 12 and it has always been an issue. These discussions are nothing new.
It doesn't matter if you're using die-cut cardboard pieces on a printed map sitting physically across a table from each other, or pixels on a screen with someone across the globe. The issue is pretty much the same either way: the smaller the base unit the less the abstraction and, while able to get closer, to historical accuracy, it still will never be exact. Nit picking over what is and isn't abstracted vs modeled when it comes to pieces representing the size units we are using is an exercise in futility -- even if it is fun sometimes.
On this level we can't choose whether we give the division 75 mm field guns or 150 mm howitzers in the line, nor can we decide if or companies are made up of 8-man squads as the Germans used or the 10- to 12-man squads of the Russian army. Since you are leading the war effort of an entire country it is below your pay grade. We can't add LMG, HMG, Inf AT (75, 76, 50 or 37 mm) or 50 mm as opposed to 88 mm mortar teams in our forces because, to put it simply, that is too far below the level of the game to be of any consideration. If you want to play on that level of tactical operations then buy a game suitable to that style of play. Pushing that crap is just looking for more shit to argue about and confuse the basic issue and is unworthy of intelligent gamers, which I like to assume most of us are.
The basic issue is: what is a gamey set up and what isn't. The rest is just BS.
The US Army in WW II had 91 Divisions containing approximately 15,000 soldiers each. This was the division structure of the infantry 1942.
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German Infantry Division of 1940 with 17,000 men
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This is the level of the game's design. If you use these layouts, or close to them, in your Division level formations you are at least close to historical. If you use some massively larger formation, whatever you are using as your justification, you are not. It isn't number of men, number of guns, number of anything include width. It is how many of what type of subformation you use to represent the division formation that make historic sense.
It is an unfortunate aspect of the game that PDX made 80 the standard width. Although we would have a similar issue if they had said any number equally divisible by 15, or 12, or probably even 13. They could probably even made the division templates 4x4 instead of 5x5, but they didn't and we're stuck with it.
I know this was too long for many of you to bother reading. Sorry about that.
While you are making good points, your final example is contradicting everything you said before.
MHV has the number of infantry and artillery Battalions wrong (+2 INF, +1 ART), doesn't show the AT battalion (and given the organic AT of each regiment, we could argue for 2 AT).
And it's still 38w! Where is the essential difference to 40w? What would constitute a 'massively larger' formation?
Of course this is all nitpicking, Keitel won't use the Nazi timemachine to reprimand any of us, but I find the arguments put forward very much flawed and hand wavey.
Is 40w gamey? No, because you need to pay for it with equipment. Space marines are different, because you exploit the armour mechanic, even though they are easily countered.
Pure Inf with CAS would be gamey too.
Then again, vs AI, having a brain, one eye and an index finger could be considered gamey.
My point still stands: depending on what is your definition of historical, the game allows to build historical 22-40w divisions and there is no solid argument to denounce either as ahistorical.
Certainly, some 27-33w looks like the design target for ww2 divisions in hoi4, but that is deliberate.