So, just to recap: from all that we know from the discussions in this thread, we can conclude:
1. Gene Roddenberry wanted all starship personnel to wear the delta and all Starfleet Command personnel to wear the flowery star. While the delta was an original design from who knows where, the flowery star was something sold in a craft shop, and is in fact still commercially available today.
2. During the run-up to the production of "The Doomsday Machine," Bill Theiss, apparently unaware of the dictate regarding starship personnel, decided the character of Matt Decker needed a unique patch, representing that he was in fact from a starship other than the Enterprise. Somehow, this went unnoticed by the powers that be, and in Theiss mind, the concept that each starship had its own unique patch was validated.
3. That validation led Theiss to design a third starship patch for use in "The Omega Glory," which we see on the uniform worn by Morgan Woodward during his memorable portrayal of Capt Ronald Tracey, as well as Dr. Carter, the Exeter's late Chief Medical Officer (and a full commander... why wasn't McCoy one too?). However, during dailies, Bob Justman, who somehow didn't watch daillies featuring William Windom during the (I'm guessing) 3 or 4 days he was filmed during TDM (based on the varied beard growth seen), notices Tracey's patch and raises the red flag, quickly sending off a "what kind of fool are you" memo to Theiss, reminding him that all starship personnel are supposed to wear the delta regardless of the ship on which they serve. He also realizes that there's no way they can afford to reshoot the scenes already filmed with Woodward in them, so he says not to change the patch. Being very forward thinking, perhaps he even says to himself, "Maybe, just maybe, 40 years from now, overly interested fans of the show--who don't currently show up in our crappy Neilson ratings--will passionately discuss this seeming contradiction on some type of international network... maybe like a super modern Marconi machine that maybe even looks and works like a tricorder. Cool, eh?"
4. One week later, feeling appropiately chastised by Justman's memo, Theiss decides, "well, I want to use another patch for the character playing Wesley in "The Ultimate Computer," and the only other patch I know of that's approved to use is the flowery star, so I'll just use that." During dailies, Justman recognizes that flowery star as legit (that is, GR approved), makes no fuss regarding it's use, and all is happy again in Trekville. In fact, Justman maybe even says to himself, "That'll just make those future passionate discussions all the more passionate. Damn, why can't we generate that passion now with those friggin' Neilson families???"
5. Finally, during season three, with no money to even make doubleknit uniform shirts for all the dead crewmembers shown on the Defiant during the filming of "The Tholien Web," we see the delta is on their uniforms, although they're strangely hidden from sight... the positioning of the dead bodies and even the restraining harnesses seem to be strategically determined to avoid showing patches at all... so maybe they're not even on the uniforms at all! In any case, "we're gonna get cancelled" syndrome is probably setting in, and the giveadamn quotient for minor details like patches is rapidly drowning in the tanking ratings and shrinking production budget, so at this point, any 'future passionate discussions' Justman may be pondering are long gone from his increasingly frustrated fertile mind, replaced by thoughts like "I just want to get this over with!"
That about sums it all up...