For starters, the original crew isn't going to fly because of the lack of women (and that will be a desirable audience to draw).
Technically you could probably just provide more active roles / personalities for the women already present in the original crew, as Abrams did (to some extent) with Uhura. The original series was hardly lacking in women, it just put them in mostly minor or passive roles.
All of the characters would likely be changed into something different.
There is in point of fact a lot today's television could learn from the original series in terms of rendering characters who do what Starfleet is supposed to be doing in a believable fashion. The funny thing is that believably-rendered semi-military professionals
would be something "different" (in the sense that everything old is new again), and refreshingly so, from a lot of what's currently on television.
Another point is that the future of Star Trek has been sorely outdated.
Updating the futurism -- and leaving behind tropes that started out as budget conveniences in early Trek before calcifying into traditions -- would be a major necessity.
Lastly, the tone would probably need to take a change.
I don't think this is necessarily so. I mean, I think it would be a necessity for any such concept to draw on the best of contemporary storytelling and drama and try to leave the genre better than it found it -- but that doesn't necessarily mean going in for "stereotypical anti-heroes" (which I suspect television audiences are ready for a break from, much as I love
Breaking Bad and
Game of Thrones and
House of Cards) or entirely abandoning episodic story-telling (which is still done well, if on a more sophisticated level today than in the Sixties) and drives a number of popular shows.
Probably the biggest differences from the Great Bird's day are that
a) there is a bigger range dramatically of what you can do with characters today and keep them sympathetic for the audience (the Trek format used to be nervous about treating topics, like military politics and scheming, that are actually quite interesting for audiences today), and that
b) the more or less unalloyed celebration of the American Navy in Space that formed the core of the old Trek is a harder sell now (as is anything reminiscent of the American military in an era not only post-Vietnam, but also post-Iraq War). This I think is one of the key reasons the NuTrek characters are so un-military; it's not that Abrams is a twerp hipster who doesn't understand discipline or professionalism, it's more probably that he was calculating (and with some justification if so) that the straight-ahead military heroism of TOS Kirk and company would arguably seem cornball to audiences today.
Fortunately it would be perfectly possible to re-conceive Starfleet as an avatar of truly international achievement instead of as America Writ Large across space. All you'd have to do is learn from modern film and television that updates the image of sympathetic military leadership and its struggles for modern audiences (
Crimson Tide,
Hunt for Red October,
K-19: The Widowmaker [despite its unfortunate title] are all good examples), and give up on the habit (some) Trek captains had of running around lecturing everybody about the superiority of the Amer- uhh, the Federation's lifestyle.
And these people would have to die and perhaps stay dead.
This, absolutely.
But with a new crew, a lot of that goes away. You can have whatever combination of people, you can have something new and fresh without pissing (as many) people off, and you could incorporate a lot of what we see in TV today. It would probably be a lot easier to write, and would open a lot more opportunities up, but the difficulty is in getting people to give a shit about Captain Nobody.
As long as the concept is fresh, and executed with a bit of verve and vision, getting audiences to care about a new cast of characters shouldn't that difficult. It's having the fresh concept, the verve and the vision that's the big hurdle. I definitely don't think Kirk and Spock are particularly necessary to any rebooted endeavour.
Indeed I might go a step further: the whole Spockogenic concept of having a character around to be The Logical One, which was reproduced in every Trek show without fail, has aged poorly (which I think is one of the key reasons NuSpock barely evinces that trait today). Nor does a modern audience necessarily need the Captain to be an avatar of White Male Privilege, which is what Kirk mostly seems to have become in the public imagination (although there was more to the original character than that).
