Wes,
you are ignoring my questions and modeled example showing the situation in
question: resonant dipole loaded and with beta match vs. full size straight,
reflecting the real life situation in question.

You believe what you want. I have showed dipole element and EZNEC model of
effect of beta match on performance of antenna: reduced gain, narrower
bandwidth. It shows the current distribution along the element and the
hairpin beta match. That current along the beta match is "taken out" of the
element and causing reduction in gain and narrower bandwidth. Model shows
that and measurements confirm that.

This is just another application of the current along the antenna coil
(loading element, hairpin, etc.), its effect on the current distribution
along the radiator and corresponding efficiency.

Believe it, or not!

73 Yuri, http://www.k3bu.us/beta_match.htm