There is a general belief that a balun should be used where coax connects to
the feedpoint of a 1/2-wave dipole (for example), to avoid RF current on the
outer surface of the coax outer conductor -- which can affect antenna input
match, radiation pattern etc.

But does even a perfect balun fully remove these effects? The outside of
the outer conductor of the coax feedline still will be coupled into the
received and/or radiated fields, even when there is no current flowing into
the coax outer conductor via a metallic connection directly with the dipole
itself.

As an illustration of this, consider the effect of a 1/2-wave dipole
suspended near, and parallel to another 1/2-wave dipole. Only one dipole is
driven. For simplicity of concept, let's say the active RF device (either a
tx or rx) is a physically small unit built in to the center insulator of the
driven dipole, e.g., no feedline. Standard equations, and NEC-2 analysis
show that considerable interaction exists between the two dipoles. The
input match of the driven dipole changes, and the radiation pattern of the
simple dipole is strongly affected. Yet the only coupling between these two
dipoles is by radiation.

So how important is the balun in the total RF system?

RF