We're talking about two different things here:
1. A box being used to check depth. You touch it and go.
2. A box being used to allow you to sit back further, pause and then use your glutes and hams to pull yourself up.
Unless you have problems judging your depth then type 2 should be your default. If you're a raw lifter then you need to use the box more sparingly. If you're geared then the box will help more. I would also say that on the Westside template using the box on speed day allows me to squat twice per week and reduces soreness allowing me to go heavier on the second speed session.