And the whole "Starfleet adopted the Enterprise insignia to honor the ship" around the time of TMP has nver sat well with me, either.
Yeah, I hate that idea. It's rather insulting to the rest of Starfleet to single one ship out for special recognition. And it's mistaking our perspective as viewers for the perspective of people in-universe. We see the Enterprise
as central because we're watching a show that chooses to focus on it. But it stands to reason that other starships and their crews are doing equally heroic and important things elsewhere, and are just as worthy of recognition.
And of course it never worked as a theory, because we know from "Court-martial" that other ships used the arrowhead during TOS. And now VGR, ENT, and the Abrams movies have all given us instances of its use by other ships and organizations before NCC-1701.