Why a mistake?
I get what you're saying about this being a game, and that balance is WAY more important than historical accuracy. As a "historical accuracy" guy, I'll nevertheless absolutely agree that balance comes FIRST, period.
But obviously you don't need red vs blue equipment sets to have side balance. Post Scritpum is a nicely balanced game (after some trial and error), despite the fact that all US riflemen can choose the M1Garand as default, but German riflemen are restricted to Kar98k only. Yet the sides most definitely *are* balanced overall, as anyone who plays that game would acknowledge. This was achieved through clever choices in terms of *overall* equipment sets rather than on a per-weapon basis.
I see zero need to balance on a weapon-per-weapon basis; we don't need to be hypothetical about the consequences, like I said, we can look at how things worked out in other games. So while I agree with the mosizlak doctrine (balance trumps historical accuracy, always), I see no reason that the STG44 needs an "equal" (especially since it had none!)... I think the way they did it in PS was to use total ROF (from infantry; how many total rounds either side can put out per soldier per unit time) as one measure for balance...