Mr. Bennett is correct in terms of the literal definition of flagship (no, Chemahkuu, it makes no difference whether the errand is diplomatic or otherwise).
Which is to say, yes, damn near everybody who refers to any Enterprise as a "flagship" is getting it wrong, at least in literal terms.
Mr. Bennett is also correct about why the original 1701, after multiple refits, was sacrificed: We got Spock back, but it cost us the Enterprise, and it cost us David Marcus.
David Gerrold did a whole column in Starlog about how killing off a character and then bringing that character back gets really old, really fast, and trivializes both life and death. It's fine for Bugs Bunny, at the end of What's Opera, Doc, but this isn't a Warner Bros. cartoon, and it's not being played for laughs. Tasha Yar is still dead, at least in the Prime Universe, and so are Lee Kelso, Gary Mitchell, Elizabeth Dehner, and Chancellor Gorkon. Even M*A*S*H, although it was nominally a sitcom, did not bring back Henry Blake after killing him off.
And count me among those who were not particularly happy about the Abramsverse 1701. The exterior, the interiors, and the whole business of building it intact in the middle of Iowa, while Kirk is a juvenile delinquent teen because his father wasn't around even to write him letters, instead of assembling it in orbit, from pieces constructed in the Bay Area. (As far as I'm concerned, the only plausible backstory for building a ship in a cornfield is that the Kelvin incident scared the living crap out of the Federation, causing them to react by delaying the Constitution class, building it bigger, building it more heavily armed, and building it on the ground, where it might be slightly easier to hide.)