Clearly in a center-fed half-wave dipole, if there is no load at the
center, the current there is quite low, and depends on the capacitance
from wire end to wire end. If you short across the feedpoint, it will
be resonant and the center will be a current node.

In the case of coupled microstrip hybrids, maximum coupling occurs at
odd multiples of 1/4 wavelength, and falls to zero at even multiples of
1/4 wavelength -- that is, at multiples of 1/2 wavelength. If you
DON'T properly terminate one end of the coupled line, you'll loose
directivity because of reflections at that end.

I suspect that if you include the propagation velocity of the
microstrip, you'll find that it's not a half-wave long.

Cheers,
Tom