^^This.
If the cartridge is moving with the stylus it will have less output. But it isn't; its mass and that of the arm is magnitudes higher than the stylus and cantilever. At any given instant the arm is relatively still so in fact the stylus is moving in the groove with respect to the cartridge body.
The more the system deviates from this simple fact the more coloration it will have. Decouple the cartridge from the arm, even if that decoupling provides some damping, and you increase coloration. If you want to damp the arm the place to put that is probably on the top side of the headshell so while the cartridge is properly coupled to the arm, any excess vibration (which really shouldn't be there in theory; the better the arm the more it approaches this ideal) can be damped.
I recommend for anyone engaging in this sort of stuff if you really want to know what's going on, study the engineering of turntables, arms and cartridges and then build one that works. That is what I did; its how I can state with absolute certainty that the best turntable and pickup will have the platter rigidly coupled to the base of the arm and neither the bearings of the platter or arm will have any slop. Further, the plinth will be dead and massive so it can resist airborne vibration. The rigidity is there so if there is vibration transmitted to the turntable system from its platform or the like the pickup will be unable to transduce it. And finally of course the tonearm is also rigid and dead (arm tube is damped) so the cartridge, which is rigidly coupled to the arm, can do its job.
If you deviate from this ideal there will be coloration plain and simple no ifs and or buts.
Some years back a friend of mine developed the Analog Survival Kit which was sold by Sumiko. It was basically a polymer wrap for the arm tube that allowed you to damp the arm tube of vibration. It worked because it did not interfere with the coupling between the arm and cartridge. You did have to be careful about effective mass and resulting mechanical resonance though.
One of the most challenging issues I had to face as a manufacturer was how to establish a reference. What was I hearing when I played any recording? How much of the coloration in my system was influencing what I thought I was hearing? That was tricky and the only way I could figure my way out of it was thru professional recording equipment, which I had to assume was competent since it made the recordings we listen to. So we got some mics and I had a musician play in front of them and we compared what we heard to the mic feed in the stereo. This taught us very quickly what was going on. Since I've been running a recording studio since the 1970s (Steve Tibbetts recorded 'Yr' in my first one) I've had access to master tapes which I've often used for reference.
My point here is you have to know what you are hearing. If there are colorations in your system of which you are unaware, its very common to introduce other colorations that might seem as if you are approaching a more neutral presentation. But IME synergies don't work; you're far better off if each bit of your system stands on its own merits and does not need the brightness or darkness of another component in order to work.
