Should the root bone be animated to follow a straight path?

I’m creating some animations to be used for distance matching and motion matching for my project, and I currently have the root bone constrained to follow the projected position of the pelvis bone on the ground. After I’ve completed the majority of cleanup/touchup, should I edit the root bone to follow a straight path?

For example, if I’m creating a simple jog forward animation, the character moves side to side a bit during the jog, so the root (when constrained to the pelvis) also moves side to side. Should I edit the root to follow an exactly straight path in the forward direction?

I’m new to animating, so I’m wanting to make sure I create animations to the standard used in game dev.