Fun fact! The Riflemen actually have dialogue lines for an upgrade that gives them the .30cal. Was there ever such an upgrade, or is that just a unused audio file that was never needed?
Anyway, I still think it would be a good idea. Since the M1919s don't show up until 3CP, it wouldn't be some kind of OP opening if they were field upgrades.
I think the M1919A6 in particular should be a field upgrade for Riflemen squads, similar to how Grenadiers get their single MG-42, rather than a weapon rack. After all, who the heck gives it to the Captain or Lieutenant, who are already optimized for short-mid AI (Lt) or light AT (Cpt).