I agree in real life it would be different, unfortunately though there are rules here that go against what is real. (Cant use PDA with gun out, doesn't make sense but its a rule, can't run whilst escorting someone, doesn't make sense but its a rule) etc etc.
Imagine trying to hold the steering wheel with a full size assault rifle in your hand, that barrel be smashing through the windscreen and how you going to be shifting gears and turning the wheel with a shotgun in your hand.
Just thinking logically here