The bearing ideally should not have to transfer any mechanical energy. If it does, this means that the arm and cartridge are mismatched (effective mass is incorrect).Strongly disagree. The effective mass/compliance relationship tells us only how a cartridge/arm behave when considered as a spring-loaded system. It tells us nothing about how they respond to internal vibrations.
No cartridge is 100% efficient as a transducer. All cartridges respond to cantilever movements by:
1) converting some of this mechanical energy to electrical signal;
2) converting some of this mechanical energy to heat; and
3) not converting some of this mechanical energy at all, which remains in its original state as physical vibrations.
The mix of 1, 2 and 3 is unique to each cartridge and varies according to frequency across the entire audible band (and beyond). The portion that remains as mechanical vibration may propagate through the cartridge body, into the headshell, into the tonearm and beyond.
Depending on frequency and phase, some of these vibrations will be reflected by material boundary layers, potentially setting up internal resonances. (This is very audible with certain cartridges, like those ZYX models with a blue ball on the front.)
Other vibrations may be dissipated as heat as they travel through various materials in the cartridge body, headshell or tonearm. (Well engineered wood tonearm wands are especially good at this.)
Still other vibrations may travel the length of the arm and reach the bearings. At this point, Bpd24's question comes into effect... how will the bearings respond to this?
Some bearings (Schroeder, Well Tempered) are designed to absorb/dissipate such energies. They do so to a greater or lesser degree, but inevitably suffer some loss in precision and dynamics. Other bearings (Triplanar, SME, other fixed bearings) may pass some energies into the arm base, while reflecting others.
No single bearing parameter (including hardness) is sufficient to predict the behavior of this highly complex process, which occurs across a nearly infinite number of frequencies. In particular, the compliance/effective mass relationship has no relevance in this area.