To nobody in particular.

If the propagation time along a coil is equal to the time taken for
the current to travel along the length of wire in the coil at the
velocity of light, then, at a given frequency, if a half-wavelength of
wire is wound into a coil it should become self-resonant at that
frequency.

But it isn't. The coil resonates at a different frequency which
depends on the length and diameter of the coil as well as on the
length of wire.

Just make a coil, measure its resonant frequency, then measure the
length of wire it contains. There will be no direct relationship
between resonant frequency and length of wire.

The same experiment can be carried out using pencil and paper.

The resonant frequency will be directly related to wire length only
when the coil is stretched out straight. And only then.
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Reg.