Tom, W8JI wrote:
"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."

Are any famous authors protagonists of that theory?

One author, Bill Orr, W6SAI writes in the 22nd edition of "Radio
Handbook" on page 5.11:
"Spaced closely around the beam (in a TWT) is a circuit, in this case a
helix of tightly wound wire, capable of propagating a slow wave. The r-f
energy travels along the wire at the velocity of light but, because of
the helical path, the energy progresses along the length of the tube at
a considerably lower velocity that is determined by the pitch of the
helix.

Maybe Varian has a paper on this (just my speculation).

Best regards, Richard Harrison, KB5WZI