The lower the compliance of the cartridge stylus’ suspension, the more the energy from that cartridge is transmitted into the arm. The stiffer and more damped the arm tube, the more it resists resonating from the energy being pumped into it. Also, the stiffer the tube, the higher in Hz is it’s own resonant frequency, and the more damped it is, the lower the Q of that resonance---a broader, more shallow resonant profile. The energy fed into the arm tube migrates to the back end, where it is transmitted into the arm’s bearing(s). The better the bearing(s), the less they rattle or create chatter---noise, which decreases transparency and resolution.
The arm’s designer has to balance all the competing demands, making compromises to achieve over-all best performance and sound. Applying after-market damping to an arm may upset that balance, actually decreasing the sound quality the arm can provide.
The best way to damp a tonearm/cartridge is at the headshell, as is done in the unique Townshend Audio Rock turntable.