Tactical error doesn't justify non-inclusion, in real life better tactics are used by-and-large they managed to see a need to include the gun. The Sherman includes a 12.7mm AA gun but if the Luftwaffe showed up something would obviously be wrong. It's also hard to imagine that a crew wouldn't procure something to defend themselves with regardless of whether it's the MG34 or not.
Especially in bocage where it would be easy to be flanked even accidentally I wouldn't think they'd want to be caught with their pants down, a certain percentage of Tigers include an MP40 because of the MP40 racks it seems logical to include a self defense weapon at some probability, heck CMSF crews are fully armed on the US side and I can't contemplate where all four crew can house M4s and 500 rounds in the M1.