A 1px bob actually sounds more sensible for a calm girly walk, yeah.
In Probotector the character runs pretty wildly indeed. When running, the gun will move while held in diagonally front of the chest, unless the player shoots. Then the gun held statically in the direction of the aim. In the case of a diagonal aim the torso will twist a bit to the side.
Probotector always had this perspective thing going on. I never quite liked it, but I suppose it allows the artist to avoid stale 90 degree ortho views. Metal Slug has the characters a bit turned towards the viewer, and it works quite well.
I made an angle view of a turret recently.
Of course, when a character holds a rifle, the torso will have to twist a bit towards the viewer. Tanks and turrets don't have reason to do that (other than striking a stylish pose).