Indeed it is a badly written mish-mash of an explanation.

Your response, OTOH, is very lucid. Well done!

Not having seen any slo-mo films or videos of casting, I would guess,
and did guess, that the rod would have about the same amount of
bend--and thus effective length-- during most of the forward stroke.

All the well-known casting gurus, Lefty Kreh, Joan Wulff, Mel
Krieger will tell you that the optimum rod tip path is a straight line...

Never had the opportunity to hear them say that, but I can see the
logical reason for it.

and there is plenty of video to back them up.

Do you mean their rod tips actually describe a straight line?

Seems to me, a priori, that with a given rod and line, only one length
of cast (and therefore amount of casting effort) would achieve that. A
longer cast, or a shorter cast, would produce different results.

vince