As a newcomer to the group I'm hesitant to join a discussion which has
been running for almost 200 postings, and where the protagonists
understand the topic in much greater depth than I do. But here
goes ....

My starting assumption is that EZNEC can model a helical inductor
reasonably accurately, with the exception of the increase in AC
resitance caused by proximity effects.

If I take an EZNEC model of a coil - 40 turns #14 wire, 6" diameter,
12" long - I discover it has a characteristic impedance of about 2550
ohms at a self-resonant frequency of around 6.1 MHz. If I use it as
the base loading coil for a short vertical antenna with a 6ft whip
above it, I notice that EZNEC shows a difference in the current at the
top of the coil compared with the bottom of about 0.69:1, and a
resonant frequency of 3.79MHz.

I then look to see which of the various models might reasonably
predict the values observed in the EZNEC modelling.

Clearly, a simple lumped-element inductor doesn't get close. I've read
various web pages and postings which argue qualitatively that things
like "distributed capacitance" might explain some of the observations,
but as yet I've seen no quantitative analysis which attempts to
predict the numbers.

In contrast, I look at the work of Corum & Corum and of G3YNH who
insist that "coils are best regarded as transmission lines", and I get
quantitative results which closely match the EZNEC results. For my
example coil, I get a self resonant frequency of 6.3MHz (cf 6.1MHz),
a characteristic impedance of 2792 ohms (cf 2550 ohms) and an Iout/Iin
ratio of 0.72 (cf 0.69)

Not only that, the transmission line model predicts an inductive
reactance very close to that needed for antenna resonance at 3.79 MHz

I'm a simple soul, and I don't pretend to understand all the maths
involved; I merely observe that the transmission line approach
delivers "hard numbers" that closely match those predicted by EZNEC.
I've yet to see another model get close. So, until I do, I guess I
have to favour the approach of Corum & Corum, G3YNH et al.

If someone can show me similarly accurate results from an approach
based on a lumped-element model, I'd be interested to see them.

Steve G3TXQ