@Ronald Raygun

if we wanted to reduce the power to zero, we'd need to put
through an infinite amount of mass each second.

That's correct -- that's exactly what and infinitely large propeller I
described would do.

This is clearly unachievable,

That's correct, many illustrative physics thought experiments are
unachievable -- that does not mean however that they are not
theoretically correct.

and so I must reject your analogy with the two-by-four plank
leaning against the wall, until such time as you can
produce a 2X4 of infinite length and zero density. *:-)

You just conceded that a propeller can theoretically produce 10lbs of
force while consuming 0hp. The 2x4 can also do this. Sound
comparison. QED