from the cartridge POV, how can 3Ω be different than 3Ω? I am speaking primarily about the effects of the load on the electromechanical behavior of the cartridge and what impact that may have on the sound.
You are correct in your conclusion, but IMO asking the wrong question. Rather than looking at it from the cartridge's perspective, consider the pre-amp's perspective. The pre-amp is the device that will be passing along a signal to the next component in the system. Both IV and traditional preamps "see" the entire "electromechanical behavior of the cartridge" but neither pays attention to the full set of that behavior. One type of circuit pays attention primarily to the current, and the other, voltage. Thus the two methods can look at a cartridge behaving in very different ways but end up paying attention to--and passing along--signals that are similar in character; i.e., if the cartridge's current under heavy load is similar in character to its voltage under a light load, expect an IV preamp to pick up a similar signal from the cartridge through its low impedance input terminals as a traditional preamp would through its high impedance (and lightly loaded) input terminals.