From: US Midwest
I will take on the AA part. The Germans, at least, employed large formations of Luftwaffe Flak troops, "Flak Corps", so the units do not appear to be ahistorical in and of themselves.
In game terms, they do operate differently than a unit's indigenous AA, so there is not an exact duplication there game mechanic-wise. Maybe the added level of protection they provide is overkill, but I think it evolved from the dominant position aircraft had in this game for a long time. You would have to be careful scaling it back, unintended game balance issues are sure to crop up.
The Flak Corps were frequently pressed into ground combat(especially in the Anti-tank role), so again the Germans have a historical basis for their units. These were very effective defensive units, in fact, I wouldn't mind seeing them be more effective against armor then they currently are.
I would have to do some research to determine if the other powers used units like this. In this game, if a country did not historically field a unit, it does not show up as available to buy on their menu, like the US can't buy Mechanized Infantry. If no historical basis can be found for the other powers fielding large-scale mobile AA units, you could make an argument that AA units should be deleted from the applicable menus. These countries would then have to rely on their units indigenous AA for defense, as you suggest. Game balance, however, is likely to raise it's ugly head once again. Could you defend against a Sealion with no AA units? Could the Soviets slow down the Blitzkrieg without AA units? Both are likely to be problematic..
I suppose you could argue that for all that they do, they are too cheap at only 100mpps. But their inability to attack makes the cost appropriate, I think. They are completely passive. Or, if placed in a frontal position in a defensive line, maybe passive-aggressive at worst.
AA units are not completely realistic, I will grant you, but adding this bit of reality will cause more problems than it will fix, I believe. And the Germans would have to keep their units in any case, to be fair, as they really had them.
Lock up your wife and children now,
It's time to wield the blade..