As for the insignias representing the fleets, I've felt for a long time that that was more likely than having a different one for each individual ship, since we saw a lot of non-Enterprise personnel wearing the arrowhead in "Court-martial."
Apparantly, it was never intended for there to be individual ship insignia in TOS, at least according to Mr. Justman:
TO: Bill Theiss
FROM: Bob Justman
SUBJECT: STARSHIP EMBLEMS
DATE: December 18, 1967
Whilst sitting in Dailies today, it was noticed that a Starship Captain (from another Starship) was wearing an emblem unfamiliar to yours truly. I have checked the occurences out with Mr. Roddenberry, who has reassured me that all Starship personnel wear the Starship emblem that we have established for our Enterprise Crew Members to wear.
Doubtless this situation has arisen due to the fact that a different Starship emblem was used last season on “CHARLIE X”. However, the personnel of that other ship in that show were the equivalent of merchant marine or freighter personnel -- and therefore not entitled to bear this proud insignia on their individual and collective breasts.
Please do not do anything to correct this understandable mistake in the present episode. However, should we have Starfleet personnel in any other episodes, please make certain that they were the proper emblem.
Under penalty of death!
Signed this 18th day of December, in the year of our Lord, 1967, by
ROBERT H. JUSTMAN
CC: Gene Roddenberry
John M. Lucas
P.S. A carven “I’m sorry!” will be sufficient.
This memo was quoted in another thread elsewhere earlier this year, but I do not know it's source/origin beyond that.