the amount of capacitance "needed" to smoothe out rectified AC voltage into DC voltage is inversely proportional to the final DC voltage that is delivered to the circuit
You are strictly correct, you did not post a formula in full. I took what you wrote to be the same thing as a formula, where the constant of proportionality is not specified.
Unfortunately, it is far from the full story because the more capacitance you add for a given final voltage, the lower the ripple.
Thinking about reducing ripple, I wondered about using a Class A amplifier being fed a constant signal. The output should be constant voltage, whatever the load. An over-the-top-solution maybe, but then I remembered that Wilson Benesch use three Class A amplifiers, one for each phase, to power their megabuck direct drive turntable.

