In this context, is there any relationship between cartridge bandwidth and cantilever stiffness?
The stiffness is a function of the load impedance. Obviously it will be more supple if loaded at 47KOhms as opposed to 100Ohms!
This says nothing about the bandwidth of the cartridge itself, which would be unaffected by the load. However, the stylus has mass and to trace high frequencies must be low enough that its mass is easily moved by the modulations in the groove. Adding stiffness to the stylus support isn't going to help- at some high frequency (which may well be outside the audio band) the stylus will no longer be able to keep up. This does not take much to sort out.
Any modern cutter has bandwidth well outside the audio band. We use a Westerex 3D cutterhead, which was designed in the 1960s and it has bandwidth to 42KHz, at which point its bandwidth is intentionally limited by the electronics.
We can cut a 30KHz tone on a lacquer and play it back on some pretty conventional LP equipment- for that we use a Grado Gold mounted to an older Technics SL1200, the idea being that any cut we make should be playable on that machine. Its got no worries playing a 30KHz tone, but if we start loading the cartridge we can see the output level drop (with some distortion/noise apparently added), whereas at lower frequencies its still perfectly flat (once equalized).
Empirically speaking its easy to deduce that the load is affecting the ability of the stylus to trace the groove, which is why we see distortion as essentially the stylus is mistracking.
Even though there is no microphone that has bandwidth that high, it seems a good idea to keep the stylus as planted in the groove as it possibly can be. So IMO its important that the phono section be immune to the RFI generated by a LOMC cartridge so a 47KOhm load be used to allow the cartridge to track to the best of its ability.
BTW, if an SUT is employed, you can side step this issue a bit as most SUTs lack the bandwidth to pass a 1MHz or even 200KHz noise source which can be really helpful to many phono sections! IMO this might be why SUTs have a certain following.