David wrote:
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.

Yes.

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.

There is no standing wave on the antenna. The distribution patterns of
voltage and current on a half-wave dipole shown in antenna books, is not
a standing wave. They are the RMS values of voltage and current along
the dipole. At the centre, the ratio of Vrms to Irms is 50 ohms.
Alan