Maybe, but we find out about Garth during the five year mission, and Kirk has another 20-30 years of a career after that, where he saves Earth from V'Ger, the Federation from Khan, saves Earth again from the probe looking for the whales, and prevents an all out war with the Klingons. I don't think it's a "mistake" to say he was the greatest captain whoever lived.
Sure, but who knows what extraordinary feats were performed by the other captains whose adventures we didn't follow? The thing is, I've never liked the tendency to assume that the specific people we watch on TV every week are the only ones who ever actually do anything. Realistically, other starship crews should be having equally extraordinary adventures, saving planets and defeating cosmic threats and doing stuff that's just as impressive. After all, they all went to the same academy, got the same training. They can't
all be inept enough to get themselves killed like the
Constellation and
Exeter crews. The other captains can't
all be as unstable as Garth or Decker or Tracey.
I just feel that when the main characters are focused on exclusively, as if they're the only ones in the universe who had any accomplishments of note, it undermines the credibility of the story and makes it feel more like a story, like a finite imagined world with nothing going on except what we see on camera. I'd rather see the show placed into a larger context where there's a lot of stuff going on that we don't get to see, because that adds more texture and dimension to the universe. So I'd find it more plausible to see Kirk treated as
one of the great captains of the 23rd century, rather than the only one who ever gets talked about. I want him to be part of a context rather than an isolated entity.
And that's just the problem -- the writers' tendency to assume the characters are just as fannish as they are and have the same preoccupations, which makes it feel more like a fictional construct and less like a big, plausible universe. In "The Naked Now," the crew didn't have Kirk's every exploit memorized, but had to do a computer search to find a reference to Kirk's crew and their prior experience with the disease. That was more plausible to me. After all, to us, Kirk's adventures are the only thing we saw of the 23rd century, but to the 24th-century characters, they were just one small piece of a vast body of knowledge about people and events in the 23rd century. I mean, sure, there are plenty of people who could recite the career of Douglas MacArthur or whoever from memory, but there are plenty of other people who know practically nothing about the subject. (Heck, I couldn't even think of a second famous 20th-century military officer to cite as an example.)