I can see that on a flat surface the tension in the calf as the knee bends would tend to make the quads do less work.

A further couple of points on squats:

1/ do not let the knee(s) bend in towards each other - you should be able to just see the side of your big toe as you look down the inner side of your knee

2/ it is the initial taking up of tension that particularly strengthens tendons, so if going lower is difficult/painful, even those first few degrees of bend are beneficial.