Awarding individual achievements is fine. Having the entire fleet adopt just one ship's individual insignia is implicitly saying that one ship and crew are the only ones that matter.
Of course, not the entire fleet as demonstrated by the still individual insignias of
Constellation and
Exeter, but possibly Starfleet personnel ranging from base to destroyer personnel (e.g. "Court Martial" officers in Starbase club).
I assume Starfleet to have some kind of starship flagship, too.
For whatever reasons the Starfleet board of admirality convenes to select a starship as flagship
and adopt that starship's insignia for its (non-starship) uniforms for the next years is up to our imagination.
We could assume that Starfleet really liked how Captain Christopher Pike handled critical situations and conducted first contacts. Starfleet would like to see other starship captains to take his example as an inspiration because it reflects the policy Starfleet has in mind for the upcoming years.
Adopting an individual ship's insignia as a visual sign for this policy doesn't seem to be a weird concept, IMHO.
Further, it could be completely out of control of a starship's captain (which would take some steam out of the "disrespectful competition" debate).
Let's say Starfleet would like to see a more straightforward approach for the next years as displayed by Captain ... of he Starship... - that's the insignia chosen. Starfleet would like to see a more cautious approach as displayed by Captain ... of the Starship ... - then that's the insignia chosen.
Besides, it's fannish. It undermines the reality of the fictional world by superimposing our perception of the Enterprise as the center of all things.
That's not true. From what we can rationalize it could look like this:
- delta insignia of Enterprise under Captain Pike prior to events in TOS (being phased out by the time of "Court-Martial" and "The Menagerie" and being replaced by)
- flower insignia of Lexington under Captain Wesley (promoted to Commodore by the time of "The Ultimate Computer")
- delta insignia of (Kirk) Enterprise combined with circle insignia of unknown starship by the time of TMP
- delta insignia of (Spock?) Enterprise combined with rectangular insignia of unknown starship by the time of TWOK.
So there'd be an equal balance between
Enterprise and other starship's "accomplishments"
And of course, as we now know, it was based on a misconception. That's the crux of it: The belief that the arrowhead was unique to the Enterprise prior to TMP was simply wrong, as "Court-martial" proves. It was always meant to be fleetwide, and there's now plenty of canonical evidence affirming that it was in fleetwide use long before TOS. So there's no sense debating the legitimacy of an idea that we know is conclusively wrong.
There is no evidence in "Court-Martial" that Kirk's former classmates were serving on starships. For all we know they are still serving on the same destroyer Kirk once had been assigned to during the "Vulcanian expedition" and are jealous and envious that Kirk moved on and now even commands his own starship (and they have to wear that starship's insignia but are not part of its crew). Admittedly frustrating for them.
Let's talk about the essential issue we have here: Bob Justman was approaching the uniform's insignia from a budget-saving (and "in-universe"?) point of view and there's nothing wrong with it (actually I sympathize with his approach). However, when it came to shooting "The Doomsday Machine" and "The Omega Glory" the other producers apparently decided it would be better to go for individual starship insignias.
I can see a
practical motivation for this move: TV viewers which might have gotten late into a particular episode, would have instantly noticed that the guy Spock was arguing with in "The Doomsday Machine" was
not a member of the
Enterprise crew, neither was the guy in "The Ultimate Computer" or the guy in "The Omega Glory".
Of course, this limited a director's shooting option when placing the extras' bodies in "The Omega Glory" and "The Tholian Web" (and possible something Bob Justman was concerned about, too).
(When it comes to the delta insignia Bob Justman is the saint of TOS continuity and canon, but when he explicitly says that the other starships belong to the "Enterprise Starship Class" he is not?

Interesting, who wants cake and eat it, too?

)
Besides, the "fleetwide" basic symbol of Starfleet is
not the delta, but the
arrowhead, featured in many facilities of Starfleet onscreen and on the hull of the
Enterprise and the TAS ships.
Bob