My personal take on it is that the coil generates what you tell it to.
Leave it open it generates voltage, Load it down it generates current.
@intactaudio To be clear, a current amplifier does not significantly load the cartridge. The 'zero ohms' thing that you see talked about in reference to them refers to the virtual ground with which the cartridge plays a part. Virtual ground being nearly zero ohms is **in no way** similar to actual ground!! So the cartridge does not behave as it its driving a short. It behaves as if it is driving a fairly high impedance. This may sound counterintuitive, but a virtual ground is a thing that has to do with how OpAmps work and if it was really the same thing as zero ohms, the OpAmp wouldn't work. Another way of putting this is that 'virtual ground' is a charged term in that it does not mean 'ground' at all. The word 'virtual' means something different than 'actual' :)
when you say "ability to trace" are you referring to the output
generated by the cartridge or the physical ability for the stylus to
remain in contact with the groove wall?
I am referring to the simple fact that a stiffer cantilever will be unable to trace higher frequencies- at some point, it won't be able to follow the groove wall impressed with higher frequencies. This point may be outside of the audio band, but the way some people try to use loading resistors as a tone control, with some cartridges I suspect it will be inside the audio band too. Regardless, by loading the cartridge in a significant manner, causing the cantilever to be less supple is unavoidable.
The reason I do not think cartridge designers design for any load other than 47K is twofold: first, 47K is the industry input impedance standard for phono preamps. Second, I had a conversation with Jonathan Carr (well known of Lyra fame) on this very topic and it was he who mentioned to me that loading at 100 ohms or the like would have the effect of reducing high frequency performance (this conversation occurred in my room at the 2014 Munich show; we had both been active on a thread on cartridge loading that can be found on the 'What's Best' audio forum). This issue was at the heart of the conversation- it was not about anything else. Now as a phono preamp designer, having this conversation with a top cartridge designer, and understanding basic physics of how transducers work, this confirmed my own work in the area. He and I are on the same page with anything to do with cartridge loading, not just the cantilever stiffness issue.
If you know how electro-mechanical transducers work, you can't come to any other conclusion. To make things easier to work with, we humans often simplify a picture so we can deal with basic concepts. Making the cartridge output invariant as if it somehow does not obey Ohm's Law and basic generator theory (see
https://en.wikipedia.org/wiki/Generator_(circuit_theory)) is one of those ways of simplifying a concept. But if you understand that a cartridge is a generator, maybe this idea is easier to understand in that a conventional generator which is spun to make electricity, the generator shaft becomes progressively harder to spin the more the generator is loaded. A cartridge **has** to have a similar behavior!