^^ Concise summary in a nutshell and a theory that matches the observable facts, I like it very much.
Why only 12 ships? IIRC the US Navy had 12 aircraft carriers in the 1960's and this was an inspiration. I won't rule out the possibility that there were differences in opinion between Gene Roddenberry (12 are enough) and Bob Justman (12 are not enough).
Apparently the basic quote from "Tomorrow Is Yesterday (TY)" compelled D.C. Fontana to suggest to establish the names for the "12 ships of the starship class" included in Starfleet. Bob Justman got a copy of the proposal and wrote Gene Roddenberry which names he felt should be established for the "12 ships of the Enterprise
To me that looks like Bob Justman wanted to interpret Kirk's line in TY as 12 ships of the Enterprise Class (next to "starships" of other classes). However, the summary of the name finding process in The Making of Star Trek
reads as if [Gene Roddenberry] felt 12 are enough (could also explain "the only starship in interception range" in TMP and beyond).
It really depends how many starships Starfleet had in the first place to make an impression at the Altair VI festivities in "Amok Time". Admiral Komack wanted the Enterprise
to be one of three (next to Excalibur
). I'd speculate that a show of strength would at least require 10% of your available starships (i.e. a total of 30).
On the other hand it had been possible to draw 5 starships from active duty in the M-5 computer wargames (already tested in simulation!) in "The Ultimate Computer". I'd speculate again that you shouldn't withdraw more than 10% of your starships from active duty (i.e. a total of 50)
"United Earth Space Probe Agency"? Either Kirk didn't want to tell Captain Christopher more than he could digest or the Enterprise
was still operating under the authority of the UESPA.
Apparently it was during the times of "The Cage" and "WNM" because we can clearly see the United Earth (i.e. United Americas) insignia on overalls.
Then you have mostly Anglosaxon names for the Enterprise
However, increasing tensions with the Klingons and the Romulan Star Empire in the first TOS season could have transformed "Earth and its allies" from "NATO" to Starfleet.