Various exercises are used to develop core strength. However, most of the exercises typically recommended do not involve strengthening the core muscles through the full range of motion. Or they rely on strength exercises in which the core must remain stable, i.e., movements in which there is no movement of the spine.
There is no questioning the fact that as you do various exercises such as the squat, split squat, deadlift, good morning and overhead press you develop isometric strength of the core muscles to maintain a stable spine and with some of the exercises, an erect position. But, it is mainly the lower back muscles that are involved, not the abdominals.
When you do any of the above-mentioned exercises, you do not automatically increase the static strength needed to hold the trunk stable unless you keep adding more weight to the exercise. This also applies to doing exercises on uneven surfaces for balance.
These exercises may be good for static stability but they do not improve the dynamic strength of the core, especially of the abdominal muscles, which is needed for body movements involving flexion, extension, rotation and lateral flexion of the spine.
Developing more static strength is a far cry from what the athlete’s body needs and requires. If you do dynamic exercises for the abdominal and lower back muscles, especially through a full range of motion, you will develop the ability to hold any position needed. There will be no need for doing separate exercises to develop greater isometric strength; it will be a secondary effect of doing the exercises.
Perhaps even more importantly, you should concentrate on exercises to develop specific muscles in a dynamic manner. This applies to not only the abdominal, but also the lower back erector spinae muscles.
When done through a full range of motion you develop greater strength and at the same time develop a stronger joint that will be less prone to injury. As you do the dynamic exercise you will automatically be developing greater static strength of the muscles when they act as stabilizers.
For more information see Biomechanics and Kinesiology of Exercise