Cecil,

What you are missing is the flux inside the coil links all the turns at
light speed. When it does that, current appears at nearly the same
instant of time (light speed over the spatial distance of the inductor)
in all areas that are linked by flux.

The flux coupling also tries to equalize currents throughout every area
of the coil.

Charge conservation also dictates that any current flowing into the
coil has to be equalled by a like current flowing out the other
terminal, less any displacement currents caused by stray capacitance
(electric fields) to the outside world.

We cannot have a two terminal "black box" with confined fields that
behaves any other way, standing waves or not.

The only flaws in having zero current phase shift and zero current
difference are the less-than-perfect flux coupling and
less-than-perfect confinement of the electric field. Any deviation from
following perfect two-terminal rules are directly tied to the ratio of
load impedance on the inductor to the stray capacitance to the outside
world, and of course less than perfect flux linkage from end-to-end in
the coil.

People can often better understand the limits when things are taken to
an extreme.

Imagine a helical whip antenna. It is a very poorly constructed
"loading coil". It has nearly infinite termination impedance at the
open end, and very poor mutual coupling from turn to turn. The form
factor is very distorted, far from being equal in diameter and length.
The ratio of distributed capacitance to termination capacitance is very
large, it can be nearly infinite.

A loading inductor or helical whip like this behaves nearly like an
antenna.

The opposite would be a toroid, with a very compact form and almost
total confinement of fields. Standing waves or not, as long as it is
not near self-resonance it has evenly distributed current inside and at
each terminal.

Most well-designed efficient short antennas use a loading coil having
very nearly equal currents at each terminal. Current equality actually
is a good way to determine a properly designed loading coil.

If you can stay on topic and we process only one point at a tme, I'm
sure you will be able to learn how this works. If you see any flaw in
how I just described inductor behavior, please point it out. Once we
agree how an inductor works everything else will fall into place.

73 Tom