A rolled arm is a spiral, and a spiral in upholstery is a lesson in how much cloth a curve actually consumes.
Wrap fabric around the outside of a roll and the outer face travels much further than the inner face, which means a single flat piece of cloth cannot cover it without either wrinkling on the inside or straining on the outside. The old solution, and still the right one, is to make the arm from separate panels: an outside scroll, an inside scroll, and a shaped disc at the face of the spiral - three pieces joined on lines that follow the geometry.
The disc at the front is the piece that matters. It is cut as a true circle, and the cloth for it is worked from the centre outward, easing the fullness evenly all the way round so there is no flat spot. A carved rosette is then set at its middle, which anchors the covering at the exact point where the fullness converges and hides the one place a spiral cannot be made to lie perfectly flat.
Which is why almost every scrolled arm ever made has something at the centre of its spiral. The ornament is solving a problem.