I don't think the Klingon ambassador's line was just about the circumstances in TSFS.
The dialogue speaks for itself:
KLINGON AMBASSADOR: ...Behold! The quintessential devil in these matters! James T. Kirk, renegade and terrorist! Not only is he responsible for the murder of a Klingon crew, the theft of a Klingon vessel. See now the real plot and intentions, Even as this Federation was negotiating a peace treaty with us, Kirk was secretly developing the Genesis torpedo, conceived by Kirk's son and test detonated by the Admiral himself! The result of this awesome energy was euphemistically called 'The Genesis Planet' ...A secret base from which to launch the annihilation of the Klingon people! We demand the extradition of Kirk! We demand justice!
SAREK: Klingon justice is a unique point of view, Mister President. ...Genesis was perfectly named. The creation of life not death. The Klingons shed the first blood while attempting to possess its secrets.
KLINGON AMBASSADOR: Vulcans are well known as the intellectual puppets of this Federation!
SAREK: Your vessel did destroy U.S.S. Grissom. Your men did kill Kirk's son. Do you deny these events?
KLINGON AMBASSADOR: We deny nothing! We have the right to preserve our race!
SAREK: Do you have the right to commit murder?
FEDERATION PRESIDENT: Silence! Silence! There will be no further outbursts from the floor.
SAREK: Mister President, I have come to speak on behalf of the accused.
KLINGON AMBASSADOR: Personal bias! His son was saved by Kirk!
FEDERATION PRESIDENT: Mister Ambassador, with all respect, the Council's deliberations are over.
KLINGON AMBASSADOR: Then Kirk goes unpunished?
FEDERATION PRESIDENT: Admiral Kirk has been charged with nine violations of Starfleet regulations.
KLINGON AMBASSADOR: Starfleet regulations? That's outrageous! Remember this well. There shall be no peace as long as Kirk lives!
It was specifically Kirk's involvement with the Genesis affair that the ambassador was referring to. He couldn't possibly have made that clearer. He didn't say "We want Kirk dead because he's this almighty cosmic hero who's more important than anyone else in the Federation," he specifically cited the events of the previous two films as his reasons for declaring Kirk a war criminal.
Remember, it's Kirk chosen deliberately in TUC because of his reputation among the Klingons. I don't think captains J.T. Esteban or Terrell had the same sort of intergalactic reputation.
"Intergalactic?" Since when did the Klingons live in a different galaxy?
Anyway, glossing over the pervasive misuse of the word "intergalactic" to mean "interstellar," you're conflating two separate questions, a
specific reputation with the Klingons and a
generalized reputation as some all-powerful, godlike cosmic hero. The two are not equivalent.
Let's go to
the transcripts again:
SPOCK: We have volunteered to rendezvous with the Klingon vessel that is bringing Chancellor Gorkon to Earth, and to escort him safely through Federation space.
KIRK: Me?
C in C: Well, there are Klingons who feel the same way about the peace treaty as yourself and Admiral Cartwright. But they'll think twice about attacking the Enterprise under your command.
...
KIRK: We volunteered?
SPOCK: There's an old Vulcan proverb. 'Only Nixon could go to China.'
Kirk was chosen for several reasons. One, implicitly, is his connection to Spock, who was the chief negotiator of the conference. Another is that he's known for his hostility toward the Klingons --
as a result of the events of TSFS. He's a hardliner, and thus his willingness to participate in the negotiations would be symbolically important at persuading Klingon hardliners to participate.
Note that the same goes for Admiral Cartwright, but he's not a starship commander, so he couldn't be the one to go. And yes, he's sent because the Klingons are aware of his reputation as an effective military commander that they'd think twice before attacking. But that's not the same thing as the whole galaxy being lost in fangasms about how wonderful James T. Kirk is. It's a military assessment of a known commander by his enemies. There are probably other Starfleet captains who have a similar military reputation among the Klingons, but Kirk was chosen because of a combination of that and other factors.
And whether the examples in GEN, DS9's TAT, etc. are "fanboy insertions" or not, they're on-screen evidence for my point that Kirk and crew are legends.
They're evidence that
by the 24th century, Kirk's reputation has been built up to a legendary status by historians. It is grossly invalid to use them as evidence of Kirk's reputation
as of 2278.
again, it's obvious that other crews have their adventures and stuff. But from the TOS movies onwards, it's pretty clear that Kirk and his crew are famous figures.
I have never denied that. What I have said, repeatedly and clearly, is that I don't accept the assumption that they're the
only famous people in the 23rd-century Starfleet, that everyone who even heard the term "Kirk" or "
Enterprise" mentioned would immediately begin waxing lyrical about their godlike magnificence.
After all, even fame is relative. Captain James Cook is famous for his "discovery" of Hawai'i, but would you seriously expect that every time you mentioned Hawai'i to any given person, they'd immediately begin raving about how awesome Captain Cook was? Every historical figure who's legendary to some is going to be unimportant to others, and probably criticized and discredited by others still. I'm sure that if I went to a bulletin board devoted to, say, the history of the English Civil War, I'd see posters praising legendary heroes that I've never even heard of, or have heard of in passing but never really given much thought to. It's a big planet, and it's only one planet. In a civilization as huge as the Federation, anyone's fame is unlikely to be universal. Someone who's admired and revered as a legend in some circles is going to be unknown to a lot of other people. That's the way it already is today in our increasingly compartmentalized pop culture (for instance, I've only recently become aware that there's a singer named Justin Bieber who seems to have been famous for a while, and I still know nothing about him beyond seeing a trailer for a movie about him recently). It's bound to be far more the case in an interstellar civilization.