A balun can reduce common mode feedline currents due to the power supplied
to the line by the transmitter, but if the feedline is immersed in an
asymmetric radiated field, how does the balun reduce/remove the resulting,
unpredictable differential current on the feedline, and its contribution
toward producing the net radiated pattern?

RF
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"Roy Lewallen" wrote:

A "non-radiating" feedline is one on which there is no net current
(i.e., no common mode current). In the case of coax, this translates to
zero current on the outside of the shield; for twinlead feedlines, it
means that the currents in the two conductors are exactly equal in
magnitude and opposite in direction.

A transmission line placed symmetrically with respect to a dipole
won't have any current induced in it, although current can be conducted
via a direct connection.

The amount of common mode current flowing in a transmission
line can be reduced by introducing an impedance to the common
mode current. It's desirable to do this without disturbing the differential
mode transmission line operation. That's the function of a balun.