The main movements people do in the gym are all linear and symmetrical. There's no increase in the range or vector of the movements, just an increase in load using the same pattern. Improving your squat numbers is awesome, but it isn't developing all the physical qualities we all want and need.
By loading irregular patterns, we can improve overall strength, flexibility, and coordination, which will actually help improve your heavier lifting and prevent overuse injuries. Stretching is helpful, but it's not enough. You need to be able to USE strength in every position your body can get into.
One simple way to start improving the strength-movement spectrum in the lower body involves using simple furniture sliders.
The multi-directional slider lunges are terrific for improving the strength and active ROM in hip adduction, abduction, hip flexion, and hip extension. All of the above movements can be done while holding onto a suspension trainer or gymnastics rings for assistance until you're comfortable doing them unassisted.