We are talking about half wavelength dipole antennas, right ?

Nic.

Methinks the situation is a little more complicated than that. The
E-field and H-field is in phase at the feedpoint of a resonant
dipole. In the real world, they are never 90 degrees out of phase,
but they get close to 90 degrees at the points midway between the
feedpoint and the ends of the resonant dipole. The E-field and H-
field are (almost) back in phase at the ends of the dipole.

The ratio of net total voltage to net total current at points along
a dipole can be thought of as a spiral on a Smith Chart. It is much
like a transmission line where the spacing between wires is too large
for the frequency of operation and therefore leaks radiation.