Reg Edwards wrote:
In the problem posed, the current is also uniformly distributed
along
the low-loss line and radiation resistance is not the value we are
familiar with and what we might do with it.

Reg, in the real world, an antenna has radiation losses so
the current decays along its length.
==============================

Yes, I know. Just insert "approximately" before "uniformly"

On a long terminated non-resonant line I guess the current falls off
crudely exponentially at a rate of about 1 dB per wavelength.

The situation is similar to that very long, low, terminated antenna
wire whose name I can't remember. And whose input resistance at LF is
about 550 ohms. Putting two of them back-to-back gives an input
resistance of twice that = 1100 ohms. Which indicates the answer to
our infinitely long dipole problem.
----
Reg.