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I have read the following:

https://www.anandtech.com/show/6068/lrdimms-rdimms-supermicros-latest-twin/2 https://en.wikipedia.org/wiki/Registered_memory https://www.pcmag.com/encyclopedia/term/62658/rdimm

Why is it that placing a hardware register, which buffers the address and command signals, in front of the integrated memory controller reduces voltage?

Naive intuition says: Whether you push the electrons to a register or the memory itself you have to move the same number of electrons. Clearly this isn't the case, but I don't understand why.

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My guess is that it's a speed issue. (The rest of this answer is not a guess...) Higher voltage means more current drive means circuits run faster. The register stage also relaxes timing. So you need either a register stage or a higher voltage for a given speed.

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Why does RDIMM-type memory require less voltage from the CPU?

It's the rise, and fall that matters -- how much rise does it take to fully charge, that matters. The same, again, for the fall.

Imagine it were an electrolytic capacitor (much the same as memory), or even a battery; it's the amount of energy thast it takes to fully charge said capacitor/battery. Before it becomes fully charged. It is at this point that it will discharge (fall).

It your case; it takes less energy fo fill, or fully charge the cell(s).

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