The idea is predicated on the assumption that it is important to reduce the amount of unwanted vibrations to a minimum. In the case of a turntable, this means reduction of the vibrations in the mechanicals of the tt, and any aerial and/or seismic intrusion. Any plinth (worthy of the name) must be able to cope with all these vibrations, reducing them to a level where they are not a problem.
As energy is said to be unable to be created or destroyed, the only only course of action is to turn vibrational energy into heat energy, by dissipation, or as we have come to call it, damping. Damping in this context can be defined as the exponential decay of vibrational energy, and although there are several ways of damping, frictional damping seems to be used the most.
So we use frictional damping to reduce the energy of the vibrations as quickly as possible, because that gives us the best chance of ensuring a 'clean signal', one that helps us with the fidelity of reproduction.
It can be shown that higher damping factor (DF) values are of the most benefit, but in reality, a value of 0.4 is a good one to aim for, as above this figure, there are diminishing returns. However, most materials used for audio structures (which need damping) fall far short of this 0.4 DF value, and most are less that 0.1. As an example, the OP mentioned Panzerholz, which has a DF of 0.6 - 0.9. By stark comparison, Corian has a DF of 0.044.
This means that a structure made of Corian would not be able to cope with vibrations at all well, and would allow these vibrations to continue to be a problem for some time (slate takes over a second to dissipate a single pulse, with a DF of 0.017, same as mdf !) whereas Panzerholz would dissipate the energy very quickly, not allowing those amplitudes to build, which is what happens with low DF materials.
HTH