Why should you not fatigue the core before performing a heavy leg workout with squats and lunges??
Intentionally fatiguing the stabilizer muscles prior to performing any exercise will increase the possibility of injury. In the case of a squat or lunge, especially when loaded, the low back will be placed at a greater risk of injury. As the stabilizers are not actually the target muscles of the squat, fatiguing them prior to the exercise provides no added benefit, but does increase the risk of injury which is exactly what you do not want to do.