An amplifier with a high damping factor may limit the total error energy in the woofer cone movement, which could be one measurement of "better", but there is no guarantee that will sound better, because the energy may be concentrated over a narrow frequency range (ringing) that is audible, compared to what happens with an amplifier with a lower damping factor. This is not a new concept, and is explored in the item linked by Nelson Pass, and has been discussed on/off since the 70's.
This is much different from a servo controlled woofer movement where the actual physical position is directly controlled, not an indirect via the coil wires (and through the cross-over).