Seriously, what's the point of telling a story about a specific group of people, if you're going to instead focus on the actions of other characters whom we aren't remotely invested in? That'd just be stupid.
Gene Siskel said:
Is this film more interesting than a documentary of the same actors having lunch?
I bring up that quote by Gene Siskel to reinforce Chardman's point because ultimately it comes down to: "Do we want to see Chekov and Sulu in action or do we want to see Extras #14 and #15 in action?" There's a pretty good reason why picking actors for supporting or recurring roles involves a much more arduous, deliberate effort than picking actors for background or extra roles. You try to get the right people for the right job, and sometimes that job means getting meatier, heavier roles that are designed to be showcased, which makes getting the right actors all the more important.
It's the same reason why half the senior staff of any given Trek show would routinely go on an away mission, even though it would wreck havoc on the ship's hierarchy if some sort of disaster struck (and often did!). It's a good thing, and ridiculously improbably lucky, senior staff rarely died on weekly away missions. Alas, once again something that happened frequently across all five Trek shows is only brought up now as a fault of, and only of, this film. But if Trek only sent down one senior staff and all red shirts (or, more realistically, an entire bunch of red shirts with the senior staff all on board), it'd get pretty boring fast. Switch it around, make a show about the lowly away team and the senior staff are all reduced to bit players, and you have a completely different show on your hands (which is fine, but such a move MUST be intentional).
To be clear, there's quite a bit to complain about in this movie, and things like NuKirk, Old Spock, and NuScotty all being so close together, or some of the humor scenes, or science and scale issues, I think that's fair game. But some of these recent "nits" are anything but, and they seem to be more concerned with finding new ways to criticize the movie than about actual plot holes, without considering things like deliberate and intentional creative licence, or the variety in human behavior. "Look at me, I'm innovative!" seems to be the intent, but it's missing the forest for the trees. Would TUC work if it was some nameless extra that caught Valeris or saved the President? What if a lone security officer who we'd never seen until the end of First Contact inexplicably knocked out Picard to go save Data from the Borg Queen? Sure, I bet anyone could argue that a decathlete security officer would be a better fighter than Picard, but does that work in the story or with the characterizations? Not at all.
It's funny, a common complaint in Trekdom was that the supporting senior staff often didn't get enough to do in the movies and TOS. Now we're complaining that the supporting senior staff is doing too much and the extras (or Pike, for that matter) aren't doing enough. So, which is it? And it's not like the movie overloaded on Sulu and Chekov, either. Sorry, but I like the fact that the writers went out of their way to make each of the Big 7 integral to eventually saving the Earth, as opposed to most of the other TOS movies. Any one could fire a torpedo at Chang or Khan, but the movie makes it clear that Chekov was the only one fast enough and smart enough (and close enough) to simultaneously compute the equations and operate the controls in time to save Kirk and Sulu on the fly.