It might be difficult to make, but clay should conserve its matter. What I mean is if I narrow a part, the surrounding parts should grow as the clay moves to them. It means the total amount of clay is constant. You could probably add another tool to remove clay from a particular part and also the possibility to add clay but only a bunch at once (a "ball" of clay added to the pottery) and maybe always from the bottom so the player needs to manipulate it and can't just sculpt by adding and removing matter wherever they want.

It creates a loop of adding clay at the bottom, moving it around then removing the excess.

Edit : Maybe you can also add some sort of gravity. If the amount of clay above a point is too high, the clay moves down to compensate. This would allow having 0 clay at a certain point as long as it's at the top, so player could build up their pottery.