Personally this just doesn’t make sense to me in canon. I think that mixing and matching should be totally possible, but that it should majorly limit the accuracy, and maybe slightly the damage.
That said, I think the OPs idea of dual wielding shotguns or commando rifles would be a bit silly. Particularly the bulldog, which I think is pump action.
Dual wielding isn’t a good idea tactically, If Spartans are the highest trained soldiers in the world I find it hard to believe they would want to dual wield.
Also the way they chicken wing out their right elbow when holding a rifle needs to be addressed. One of the first things you’re taught in the military is NOT to do that. Makes your elbow stick out further than the rest of your body and your rifle making it visible first when slicing the pie.
Dual wielding always presented a balancing issue within the franchise and would most likely present a challenge in Infinite. I loved dual wielding from the style side of things, and it’s fun to flex on the enemy players, but I wouldn’t want dual wielding in the game unless it was done well.