The main thing that differentiates Kirk from others is his personal history...
That's completely untrue. Some Trek fans may have chosen to focus on his backstory as if it's significant after the fact (after TOS was finished) but that backstory had nothing to do with making him the character that he was.
Kirk's "personal history" was fabricated for plot purposes from week to week - it was throwaway stuff in order to make a particular story work better (giving him a reason to obsess over the creature in "Obsession," for example). In truth, it was the character's current behavior within the stories as both the writing and Shatner's performance evolved over the first season of "Star Trek" that made the character who he was.
It didn't matter that he had a brother, for example, since that factoid was only introduced as a "stumper" in "What Are Little Girls Made Of" and then used as a plot point in the
very last season one episode. Never factored into a story or the character's motivation again after that, of course.
Most of Kirk's "personal history," in fact, was fabricated and used repetitiously to accomplish a single plot-oriented goal in episode after episode: to give him a prior relationship (sometimes second-hand) with a guest-starring character in the week's story and therefore motivate some conflict in a hurry early in the story.
Kirk will be Kirk in this movie if he behaves as captain of the Enterprise in a way that fans will accept as being Kirk (yep, that's deliberately recursive). That's all that's required by the character's dramatic history.
Much of what you're saying is entirely true. The key elements of Kirk's backstory (as we think of it today) were created, as you say, on the fly.
The main elements which were not are those which were created in the "series bible" (which I know you've seen and are familiar with). This was a very limited description of the man's past... more of a discussion of who he was, not how he became that person. And, in broad sweeps that could be applied to virtually any "square-jawed hero" type.
Of course, his "history" did come into play over time, and that reflected in later scripts, in how Shatner acted the role, and how various directors directed the part and how various writers wrote the part. By the time TOS was over, we knew a lot more about who this guy was, what his history was, and why he was how he was. But it was still a pretty vague history.
You're also entirely correct that most of the "backstory" we know today was created, post-TOS, to fit the character we already had, not vice-versa. But then, that's how fiction always works, isn't it?
The fact that the backstory came later doesn't mean it's not significant. Only that it came later. The backstory gives a sense of reality to the character, ultimately.. "in-universe," these are the things that explain how this guy became who he we knew all along.
The thing is, these elements... ALL of these elements... are part of who the character now is. A new character could be started, with the same "kernel" of characteristics, and could eventually become someone much different. But that character isn't the SAME character, is it?
I'm 100% in favor of a new character who's "in the spirit of Kirk." I'd just prefer that this new character wasn't being presented as a replacement for the Kirk I already know. Will that be the case in this film? I was hopeful, earlier, that it wasn't the case, but I'm a lot less hopeful now, having seen a bit of the flick, the trailer, and so forth. It's not a bad character we're being given (though the lack of comprehension of why things work as they do in a military-patterned environment is simply stunning IMHO) but it's not the SAME character.
I'd be a whole lot happier if this was "Midshipman Peter J. Bryce" and "Lieutenant Stolk" on the "USS Farragut, NCC-28432." Or if it was Ensign Robert Taylor on the USS Repulse, set in TOS times... I mean, these are different characters and different situations we're seeing. And that's ultimately where the problem is coming from. Not that it's new characters... but that the new characters are being portrayed as the ones we know.