One of the features in FPS games that can be incorporated in a unique way is the head-bob.
Idea being this: in a normal walk/trot/sprint there is a head-bob effect. But when aiming down the sights and moving, the head-bob is eliminated.
In a normal walk/trot, the head moves along its path in an up/down motion in congruence with its physical reaction to the body’s movement. Marine Corps. training teaches you to engage in a “tactical glide” when you’re attempting to aim accurately on the move. A tactical glide is simple: it’s the deliberate application of the movement of the feet paired with tight control of your upper body in a forward leaning stance, with firm control and shoulder pressure on your firearm. These things together serve to reduce bobbing to allow more accurate shot grouping while moving.
In a combat situation, this fundamental might take a back seat in favor of simply focusing on your surroundings. But I think incorporating the head-bob and tactical glide into an actual gameplay feature reflecting infantry training might be an interesting idea.