"Richard Clark"
A full wave antenna has no advantage over a half wave.
It's mismatch is very bad. No BalUn is going to fix that.
_____________

The peak, free-space gain of a full-wave linear dipole is about 1.65 dB
greater than that of a 1/2-wave dipole. Its center fed impedance is high,
but can be transformed at its feedpoint to match conventional transmission
lines.

Many AM broadcast stations use a 1/2-wave vertical monopole, which when
working against a very good radial ground system constitutes a full-wave
antenna. They do it to improve their groundwave field compared to a 1/4
wave monopole, and to reduce nighttime interference to their groundwave by
their own skywave.

But maybe the typical amateur operator would not consider these benefits
worth the effort.

RF