Lew, I dont know how you see it, or how you wrote it, but a careful reading of my post will reveal the qualifier ""conceptually" which I believe is correct.
In practice it is impossible to achieve, but the practical outcome is, IMHO, the same, the lower the internal impedance of the cartridge, the greater the transfer of current to the phono stage. And that is because the internal impedance of a cartridge will likely be well above the input impedance of a transimpedance phono stage.
https://www.stereophile.com/content/sutherland-engineering-little-loco-phono-preamplifier-measurements
And as far as semantic distinctions go, I will continue to use the term "transimpedance" as it is common usage, in the same way that SME did not invent the common headshell configuration, Ortofon did. But the convention is to refer to it as the SME headshell, so to communicate with others I observe the convention. Communication is often a messy, and imprecise, business.
BTW I am not an advocate, nor an apologist, for transimpedance phono stages. Transfer of current is hardly synonymous with good sound, except in the instance of maximizing signal to noise ratio, and my apologies if I gave the impression that it was.