But what I meant is the mechanical damping of the stylus, not electrical damping of the LC tank.Yes. If you pass a squarewave through an inductor, the more inductance there is the more it will ring; If you then place a resistance in parallel with the inductor this will cause it to ring less. When the resistance is the right value, the resulting output signal will be the closest you can get to a square wave. This resistance value is the 'critical damping' value for the inductor.
But LOMC cartridges really don't ring at audio frequencies. Now we can conclude from this that the damping of the coil is irrelevant except for the tank circuit, and the latter is of no importance unless the phono preamp has troubles with RFI at its input. But damping of the mechanism (cantilever and suspension) is a different matter, and its pretty safe to conclude that if it is damped, high frequencies will be attenuated. There are plenty of examples of this.
But I'm not sure how important this is. If the cartridge is properly set up in the arm and the arm is able to track the cartridge correctly, **and** if the phono preamp is unresponsive to RFI and is also inherently stable, then IME the stock 47K load has yielded the best results. I do think its an interesting topic though and think it bears more research.