@bpoletti It has to, Ohm's Law and such.
How much it does so is not as well researched, but I've seen a good number of audiophiles do loading by ear- essentially dialing out brightness by using a potentiometer as the loading resistor and when they felt they had it right, replaced the pot with a fixed value. I've done this myself.
But loading does not affect the output of a LOMC cartridge insofar as the coil is concerned- this is because the inductance is so low that it basically doesn't ring at audio frequencies. I know this from having passed squarewaves through such cartridges and observing the effect of the cartridge coils on an oscilloscope (BTW this is not for the faint of heart- one screwup and you could degauss the magnet or damage the coil).
So there are really only two explanations for why loading kills brightness, and stopping the ringing in the cartridge is not one of them (although in high output MM cartridges loading does affect the cartridge at audio frequencies). The two explanations are:1) the preamp is bright due to RFI; removing the RFI corrects the problem2) the cartridge is less able to respond to high frequencies due to the extra work it has to do.
The problem with the first explanation is that by varying the load, you can vary the brightness like a tone control. It should be that once the load has killed the RF resonance, that the preamp is OK. However, the peak that we are concerned about is a good 30db higher than that of the signal, and by detuning it only a little it can still have an effect. So the loading, if variable, should have a slight tone control effect. But you can load the cartridge so that its too dull... although I find that such might also just result in reduced output- a lot depends on the individual cartridge.
The problem with the second explanation is that its too disturbing. Once the RF resonance is killed, by decreasing the load value even further, we can still hear that highs are being decreased with *some* cartridges. This does suggest that the cartridge itself is becoming stiffer and less able to respond to higher frequencies. It may also mean that it does not track as well in some arms, that depending on the effective mass and resulting mechanical resonance which has been changed by the electrical loading.
IMO, this topic deserves more attention, since one of the main complaints against vinyl is ticks and pops, and one of the other complaints is the nuance required to get a proper setup. Both would be made easier if there were more light on this subject.