Wayne wrote:
Let's say I have a perfectly balanced dipole with a feedpoint impedance of
72+j0 at my frequency of interest.
I connect a perfect 72 ohm coax (an unbalanced connection) to the feedpoint,
and drive the antenna system with an unbalanced 72 ohm source.

Since the power sent to the antenna is not reflected, do I need a balun?

Baluns have nothing to do with reflections.

The purpose of a balun is to eliminate current flow on the outside
of the coax which makes the coax appear to be another element of the
antenna and thus upsetting the antenna pattern.

It also keeps RF from getting back inside the station via the coax
shield, which can cause all sorts of strange things to happen from
hot mics to computer crashes.

--
Jim Pennino