RF transmitter output has impedance of 50 ohms and is connected to dipole
with a feedpoint impedance of 50 ohms via feeder with characteristic
impedance of 50 ohms. System is perfectly matched. I expect SWR meter to
show perfect match of 1:1.

Dipole has a standing wave on it. Ends of dipole are at high voltage. Dipole
is centre-fed with centre being high current point. Standing wave means that
a reflected wave exists. Wave is reflected from open ends of dipole. What
happens to the reflected wave? How does it vanish at centre of dipole? Why
does reflected wave not go along feeder into transmitter output? There
cannot be a reflected wave on feeder because SWR is 1:1.