It's futile to speak of "continuity" within the confines of the mere three seasons that started it all - internal continuity within those was abysmal, and it's only the later patchup jobs that keep it together at all. TOS didn't offer enough material to establish a continuity that would be contradicted by added material. We only got the foundation on which to build a continuity. And the mold and moisture in that foundation, the so-called creator intent, has thankfully been evicted so that the house still stands.
We're just going to have to agree to disagree here. I enjoy fictional continuity in general and Trek continuity in particular, and I usually really enjoy your explorations into it and hypotheses about it... but I just think you're barking up the wrong tree in this case.
First of all, it is in no way, shape, or form "futile" to talk about continuity based on TOS alone. That was all anyone had (okay, with TAS handwaved in) for the first 13 years of Trek's existence, after all — the period in which Trek fandom originally
bloomed (and in which I personally discovered the show). It's inconceivable that you or anyone could sit down with a copy of Bjo Trimble's original
Star Trek Concordance and claim that there wasn't "enough material to establish a continuity." (Not to mention Stephen Whitfield's fascinating
Making of Star Trek, for behind-the-scenes details on, yes, creator intent. Or the multiple volumes of
Best of Trek books collecting countless fan articles analyzing that supposedly inadequate continuity in painstaking detail.)
It is, I would submit, only the later spin-off shows that create the
need for "patchup jobs" to keep things reasonably consistent. (Of course no fictional universe will ever be
perfectly consistent, but "reasonably" is a pretty fair goal.)
The 2009 movie doesn't ring a bell? It's no more "deviant" or "visually inconsistent" than TNG was. Or, say, the third season of TOS was.
On the contrary, it's explicitly an alternate timeline. It tells us literally nothing about the TOS era in the original universe.
And that information does not logically amount to Kirk's ship being the best of the best of the best. Heck, the "one in a million" bit already makes Kirk a bit player, not even a dime in a dozen but something literally a thousand times less special.
Oh, now you're just being pedantic.

You know perfectly well that when anyone (well, anyone except Spock) uses that phrase, they're not trying to be mathematically accurate about the share of a population of billions, they're using it to indicate "incredibly rare and precious."
As stated, in TOS, Starfleet never chooses Kirk to partake in wars at the front lines.
Umm, in TOS there
were no wars at the front lines. The closest they ever came was against the Klingons at Organia, and that was over before it started.
Besides, how does that matter? In the TNG era the
Enterprise-D was explicitly the Federation flagship, yet viewers never even learned about the war against the Cardassians until it was over, because the
Ent was never involved in it!
(And what exactly do "front lines" mean in three-dimensional interstellar space, anyway?...)
Whenever Kirk and his ship appear alongside other starships visibly comparable to his, Kirk enjoys no high ground, either in dialogue exposition or in plot action. Indeed, at least Captains Tracey and Garth are stated to be superior to Kirk in reputation....
So, when Kirk and his ship are among the other dozen very top ships and crews in the fleet, they're treated as equals? Seems fairly prestigious to me.
(We do also know, of course, that Kirk was the
youngest captain to command a starship in Starfleet history. He was highly decorated, but even so, people with more seniority would naturally have more established career records. That's not any sort of mark against the
talents and abilities of Kirk, his ship, and his crew, however.)
And for all of the "routine" missions you keep mentioning, this is still the ship that was sent to investigate the disappearing Earth Outposts along the Romulan Neutral Zone. The ship that was sent to prevent the Klingons from using Organia as a staging ground on the brink of war. That came to the rescue of the
Constellation and faced off against the Doomsday Machine. That was assigned to transport over a hundred top diplomats to the Babel Conference. That was among the handful of ships chosen to participate in the M-5 computer tests. That was sent on an actual mission through time to investigation crucial events on Earth three centuries earlier. That was given a secret assignment to infiltrate Romulan space and procure the cloaking device. Not to mention that answered countless distress calls from beyond the boundaries of explored space... shall I go on?
Long story short, I think of it this way: if there were some ship out there with a more capable crew performing more meaningful missions, then that's the ship we should have been watching the show about. I naturally assume we followed the ship that offered the most interesting stories.