Banquo, you must accept that every material is subject to vibration, it is just a question of the resonant frequency for each one. I'm not a physicist so admit I am not the best person to answer your question. But my understanding is the higher the density of a material (in general) the lower the resonance. This is why some favor high density in plinths -- to lower the resonance point below the critical 8-12 Hz range. (Which could explain why some prefer plinth less designs, if the lack of low frequency damping and a "brighter" sound better suits their systems.)
I believe this translates to tone arm mounting as well. With a secure mechanical coupling between arm and spindle/platter, material frequency differences (example aluminum and brass or acrylic) may be damped. If each stands alone, they do not damp one another, they can move independently. A further point; many do not realize the potential for urban living environmental activity. I live by a busy street. My turntable is mounted on a wall shelf for isolation. But I can put a stethoscope on the braced plywood shelf and hear traffic going by. If you have an amplifier on the same shelf as your turntable you could experience the same thing. In that environment I would not want my tonearm to be subject to micro-vibrations picked up and translated by a base that was not mechanically damped (attached) to the spindle/platter. Again, consider the extremely small movements of the stylus tip to generate signal.
I think your question on isolating the arm from table motor vibrations has two answers. A decent design will minimize motor vibrations to begin with. But if the motor is noisy, there could be an energy path from the motor, down through the shelf, then up through the freestanding arm. By the time the energy reaches the arm and then stylus, the various materials it traveled through will change its frequency, thus it will vibrate differently than the platter and record. When the arm/cartridge and spindle/platter are mechanically coupled, I believe they should at least vibrate in unison, thus minimizing the impact on the stylus in the groove.
I hope this makes some sense and perhaps another person with more technical knowledge can correct or fill in these points.