Lateral stabilization (LS – stability in the side body) is mandatory for athletic endeavors and for day to day activities. In general, many exercise programs address strength and fitness in the anterior (front) and posterior (back) parts of the body. Aesthetics trumps function in this case. However, focusing on the superficial musculature does not support developing a solid foundation from which physical actions can be performed. Improving functional fitness must include improvement of LS components.

Stabilization must occur on all sides of the body when it is moved or readjusted . . . . front, back and laterally. Bodily integrity requires muscles to synergistically interact on a consistent basis. It requires the body to be ‘in communicado’ with itself. Training the body to function ‘as a whole’ provides a base of support for the strength of the superficial muscles. A cylinder rolls in a uniform motion and simultaneously supports itself. If the body is likened to a cylinder, the body must be proportionally strong in the front/back-left/right-top/bottom. LS is critical component to overall stability.
Lateral Stabilization is an integral component for moving through space. One foot lifts as the other plants into the ground. As the lifted side of the body is propelled forward or backward, the lateral stabilization subsystems engage to maintain bodily integrity . . . to keep the body from collapsing. Movement is multiplanar: up/down, left/right, forward/backward. These dimensions must be integrated for movement to proceed in seamless fashion.

Most strength training is front body/back body oriented. The individual is either lying supine, lying prone, standing upright while moving in the sagittal plane (front to back). Lateral movement is typically trained in a mono-planar fashion. This is not bad for general strength. For better functionality, the lateral stability must be coupled synergistically with other movements for optimal training.
Improving ‘big muscle strength’ will not facilitate compensatory actions to mask inadequacies in LS. Functional training of lateral stabilization supports the expression of overall strength. For example, if pushing straight. against an object or someone and the object shifts, then LS would be needed to keep the person upright as they continue to push. Similarly, the body must respond to various force inputs in a unified manner.
Here are some exercises that address aspects of lateral stabilization. Movements such as the single leg cable rotations not only improve balance, and core stability but also engage lateral stabilization. Side planking variations are good as well. Frontal Plane Single-leg Balance Reach forces the muscles of the lateral subsystem to keep the pelvis level and the femur from excessively dropping sideways into the balancing leg.
The importance of LS cannot be overstated. it increases the integrity of the body in all planes (of motion). General movement of athletic endeavors would not occur without LS. Training regimens must include functional movements that engage LS. There is information available on the internet that expands on the importance of LS and manners in which it can be trained.
Yes!