Roy explains this in the first paragraph of that section on “Using Transmission Lines.” See the manual below. Here Roy explains how using Eznec works to solve the 3rd conductor issue, and he explains why. IMO Roy is not ignoring the facts about a third conductor. He goes on to tell us how Eznec handles this when the load is not purely resistive for some reason.
roy seems to be talking about feedlines using the tl function eddie,
im asking about the radial sleeve that forms a taperd transmission-line and is part of the antenna structure,
For a while back in the good old days I believed Freecell…when he too used to try and convince me that the cone on the S4 worked just like a coaxial feed line. He said the cone feeds the bottom end of the S4 ½ wave radiator, and thus made a smooth transition to a match for the end of the ½ wave element above. I didn’t see it and I didn’t believe it, because in order to feed the end of a ½ wave element requires a very high impedance connection. Coax presents a need for a very low impedance.
the top end of the sleeve is fairly high impedance eddie, its 30" wide with about 1" center conductor, i agree its not a smoothe taper,
coax always has equal currents on the inside eddie, it will radiate if the load is unbalanced,
and if im understanding roy correctly that radiation won't show as radiation in eznec unless you model the coax as a two wire transmission-line and add a wire to simulate the outside of the braid,
he also says nec is no good for modeling 1/4wave stubs because in the model the stub will have equal currents and no radiation but in the real world the stub will radiate due to unbalanced currents.
what does eznec see the sleeve as?
the "open sleeve antenna" article was in the arrl antenna books for years eddie,
its not new to you, i quoted from the article in the first post of the alternative viewpoint thread, we have talked about it several times,
you need to read it to understand what i mean by transmission-line mode currents and antenna mode currents with regards to the antenna they describe,
it will answer your other questions,
you could model the antenna they describe, it only has two sleeve elements, like a ssfm with two legs removed, see if you get similar numbers.