Shorting rings are monunted to the non-moving parts of a driver in order to lower flux-modulation of the magnetic assembly.
An eddy-current brake built into the voice coil would lower Qms but not any nonlinear distortion.
The voice coil former resistivity matters even with a gap. Compare Qm of drivers with fiber glass, kapton, titanium and aluminum for an indication.
A metal former can also improve heat transfer, thus increasing power rating.
I'd say it does increase a voice coil's time constant but it would not necessarily improve the power rating. Modern techniques like inside-outside coils would be better.