Bill: you said
"I'm confused: why is that a "good thing"? Most antennas are well below that value, and even a folded dipole is nominally 300 ohms at the feedpoint. Getting a higher feedpoint impedance would mean introducing reactance or using a transformer, correct?
I realize you are quoting Brian here, and this is all way above my pay grade... But, working in the audio field most of my life, I tend to equate RF with AF as they are both waves, albeit at much different frequencies. The analogy here being... transmitter tank>feedline>antenna system as compared to a horn speaker, i.e. driver>throat>horn mouth.
I would refer you to "Radio Antenna Engineering" Edmund Laport, Mcgraw-Hill 1952. In particular, chapter 4, 4.4.2 - 4.10, pages 408-425. In particular, section 4.48 on "Tapered transmission- line section as impedance-matching transformer".
PS: I think the Laport book can be found as a .pdf on the arpanet.