Gene, W4SZ wrote:
"No need to account for any mythical power in the reflected waves."

My dictionary defines reflected power as:
"The power flowing back to the generator from the load."

Maximum power theorem is defined as:
"The maximum power will be absorbed by one network from another joined
to it at two terminals, when the impedance of the receiving network is
varied, if the impedances (looking into the two networks at the
junction) are conjugates of each other."

Clearly a generator (transmitter) connected to a load through a lossless
line sees Zo of the line as its load until the instant that reflected
power returns to the generator from the load.
Suppose the round-trip delay of the line makes the reflected voltage
exactly in phase with the transmitter output. further suppose the
reflection was total so that the reflected voltage exactly equals the
transmitter output. In this special case, we might as well be connecting
identical battery cells in parallel. No current is going to flow. The
generator is seeing infinite impedance.

What is the generator load that extracts maximum power from a
transmitter? A conjugately matched load, of course. To determine the
impedance of a transmitter, one only needs to find the load which
extracts maximum power. The transmitter impedance is its conjugate.

Best regards, Richard Harrison, KB5WZI