How good can it be?

Here is a comparison between a "perfect" sling and a "perfect" piano wire support. They are exactly at the centre of gravity, no friction, no out of plane forces of any kind. This is the maximum performance if everything is perfect. The mirror is 30" diameter, 2" thick, Pyrex.
As seen in the pictures, piston, tilt, tip and defocus are removed (this time accurately) and what remasins are the aberrations. Values represent surface displacements (times 2 to get wavefront delay).
The perfect sling has 2.7 nm rms surface displacements. The perfect piano wires 5.2 nm rms. The difference is near the contact points of the PW, and is due to local concentrated stresses.
Both systems are largely within tolerances. So, if one sees astigmatism it does not depend on the choice between sling or PW. It depends on manufacturing and or settings that happen to be far from the ideal configuration.