Richard Clark wrote:
In a world of mismatches, how does it happen that the transmitter always
sees an in-phase, resistive load?"

It doesn`t. You can put a capacitor directly across its output
terminals, and the transmitter will energize the capacitor. But, a
transmission line is not a capacitor unless it is a short open circuit,
or the equivalent. A transmission line is a distributed network of
inductance and capacitance. This network transfers emergy in bucket
brigade fashion. The "brigade" presents a resistive impedance to both
the incident wave and to the reflected wave. Zo is an enforcer.

Best regards, Richard Harrison, KB5WZI