"Face balanced" has kind of morphed into being synonymous with a neutral hanging face. Because of this, the popular notion is that a face balanced putter favors a stroke that tries to move straight with no face rotation. The reality is these putters are only balance in the horizontal plane, have toe hang (3:00), and by design will not swing neutral and square.
"Toe Hang" has kind of morphed into being synonymous with a rotational face bias lending itself to an arcing shaped stroke. The rub here is that the toe does open and close, but in the exact opposite way of the popular "toe flow" idea. The heavier toe creates "toe tow". Without manipulations and compensations, the extra mass in the toe area causes it to lag closed on the backswing and lag open on the forward swing. Both face balanced and toe hanging putters do this, one is just a little more pronounced.
SBST and arcing proponents teach having the face square to the path. If that's the goal, then why would a design that works against this be considered a benefit to either shape? As a practical matter, we are just dealing with grams not pounds. So overcoming these design hurdles is easily enough done with a little extra grip pressure.
There are a few "reality balanced" putters out there that have a toe pointing to 12:00. Design wise, a totally unbiased hanging face would be the most neutral putter for any stroke shape or rotation preference.
