The CG of the club (any club) is not on the sweet spot ... its at a point in space. But the club face sweet spot is connected to the hands via the hossel and shaft not some imaginary line connecting it. If it were not constrained by hands gripping the shaft connected to the hossel, the face would want to open (not close) on the downswing as the inertia caused it to want to line up with hossel on the plane.