Is it not much easier to hit a straight putt with the club anchored to the chest/belly? It always seemed to me this took the potential for face rotation out of the stroke. I thought that was the point of the ban, force the "nerves" back into the equation. Very easy to twist the putter head a little with a conventional stroke under pressure.
Full disclosure - I've never ever tried an anchored stroke. This observation comes from watching others. The putter is moved in a piston-like fashion through the ball, as if on a two dimensional plane. Rotation of the face seems highly unlikely.
Even Kuchar's arm anchor allows for face rotation, so it does not seem the same to me.