A bigger muscle has the potential to be a stronger muscle and for this reason, training for hypertrophy is critical to long term strength. Increasing the cross-sectional size of the muscle may not yield any true improvement in strength qualities, besides improved leverages but through proper application of phase potentiation, you will take that bigger muscle and teach it to produce more force during general strength training and then hone that improved size and strength into better technique and neural qualities during a well designed peaking phase.
In this brief video, Chad Wesley Smith discusses some of his strategies for hypertrophy training in the squat, including:
-Training between 60-75% intensity for sets of 6-12 reps
-Selecting exercises that allow you to tolerate higher volumes, such as high bar or safety squat bar squats instead of low bar squats.
-Driving up total volume from week to week or phase to phase as hypertrophic gains are driven by increased volume, while strength is improved by increased intensity.