The Chuck Taylor are used for the Westside method of squatting. The reason is that the floor is spread in these. The flat sole is optimal for this type of squatting. It is a wide stance which you will have trouble getting into in a normal power rack. The monolift is optimal for this stance.
When we use the Chuck's, we only put pressure on the outsides and heal of the foot. If the toes are higher than the heal, that is great. We somewhat grip with the toes, but not much pressure is put onto them.
We are able push out to the sides without the shoes buckling. The flat sole is key to our powerlifting technique.