Since "The Omega Glory" was filmed after "The Ultimate Computer," and Bob Justman sent his now famous 'under penalty of death!' memo (basically saying "All starship members wear the same patch") to Bill Theiss on the 18th of Dec 67 ("The Ultimate Computer" finished shooting on the 14th), the answer can't be that Justman's memo influenced the selection. Even if Justman had clued Theiss in before he wrote the memo, wouldn't Theiss then have Wesley wearing the "starship arrowhead" patch?
I think the decisive question remains why they still had a unique insignia for the Exeter
Crew (Captain Tracey, senior M.D. Carter) after
Bob Justman's "death threats"...
I'd guess he was pretty upset after that and did not allocate any
budget for the Defiant
uniforms in "The Tholian Web" (so they were forced to have almost all the extras face the floor).
As to what happened to the Lexington's real captain? Maybe he was given temporary shore duty while the M-5 tests were carried out. Why not, we saw that play out--albeit under false pretenses--for "The Menagerie Part 1:"Starbase Command has assigned Captain Kirk medical rest leave until our return."
"Medical rest" suggests unfit for duty, doesn't it? Theoretically Commodore Wesley could have just monitored the war games standing next to the Lexington's
And a close up of the Lexington's
captain with a panicking Wesley pushing into the frame / taking over command would have added tension and drama to the shooting of these scenes, IMHO.
I'm not sure whether Wesley's rise to governor has to be regarded as a degradation. Let's keep in mind that Commodore Stone had himself once been a starship captain, and then spent the rest of his career overseeing repairs of starships.