Some people like the loosely damped sound of tube amps, even if it is
less accurate.

Your proposal for a Kelvin connection to a speaker isn't exactly
marketable since the amplifiers would have to be designed with a sense
input.

There are already motion feedback speakers, generally for woofers.
Typically they use a piezo accelerometer to sense the motion, not a
second coil.. Velodyne has done this for over 20 years.

I wouldn't mind infinite damping. Sounds like a good idea.