PS,
Think of a simple flashlight with a mirror and a lens.

As a simple analogy, the filament of the light is the driven element
with a mirror behind and a lens in front...a LIGHT Yagi, no?

No diff in P-in/p-out...just all light directed out of the flashlight
into a beam.

John,

You're right about the efficiency, but be careful with the flashlight
analogy. A light yagi might have ~ 200 nanometer long elements.

An 20m band reflector analogous to that in a mini maglight would have
to be 800 miles in diameter.

The analogy with respect to efficiency is fine... but there's no HF
antenna that can form a beam like that.

73,
Dan