All the officers are potentially action characters because they are trained officers. The trick is using them in scenarios where they are useful and not shoe-horning them in.. So no, Uhura should not be sent on a mission instead of security staff (unless as the officer in charge) but yes, she should be sent on a mission where her skills (computer expertise and fluent Romulan) might be of vital importance.
Right. The trick is not to put them into a situation that seems unbelievable for that character and his or her position and expertise. Giving McCoy a phaser and telling him to go shoot some Klingons doesn't make sense. Or, suiting him up to space jump down to a Romulan drilling rig would be ludicrous.
That said, McCoy certainly seems to have an action scene in the first nine minutes of the movie, but it's also one more suited to his character and wasn't intended to turn out as it did. But, I'd expect to see Sulu or Chekov, or even Uhura on Kronos with Kirk and Spock before McCoy.
Parenthetically, am I right to think that the only time we saw McCoy fire a weapon was when he killed the salt monster in "The Mantrap"?
A clasic example is Star Trek VI - despite having a ship full of engineers including some weapons experts and including Chekov who functioned as the ship's tactical officer during the second 5 year mission, Spock asks McCoy to help him modify the photon torpedo. Ok, we love McCoy but he had plenty to do in the movie - asking for his help was... illogical!
Illogical, yes. Unless Spock just needed a pair of fast and deft hands used to working under pressure to simply follow his instructions, and McCoy was around at the right time. (See, there's an explanation for everything.
Still, it really doesn't pass the "sniff test." That is, in 2013, could you imagine a ship's surgeon on a submarine assisting a technician in modifying a torpedo? Still, for sentimental reasons (last movie and giving McCoy a role in the climactic scene) it's never really bothered me.
I'm fine with Uhura apparently being bumped up in terms of action and interaction with Kirk and Spock. There's room for everyone. But in that context, her relationship with Spock should pass the sniff test, too.
In the "Star Trek Guide" for writers (from TOS), it asked the reader (potential script writer) to spot the format error in a teaser where the ship faced destruction. In the final seconds, the captain turns and hugs his female yeoman, who was standing next to him. That turned out to be the format error. The standard of believability for the producers was whether or not you could imagine something like that happening on a real naval vessel in the 1960s. That is, would it seem perfectly normal for a captain whose ship looked like it was about to be destroyed to turn to a WAVE on the bridge and give her a hug?
Based on that test, I can't imagine the scene with Uhura and Spock in the turbolift or the one on the transporter pad (which was worse IMO) because I can't see it playing out on an aircraft carrier, today in a similar time of crisis. Can you see a female sailor in 2013 whose friend is seconds from embarking on a dangerous mission come up to him and say good-by to him in front of everyone the way Uhura did to Spock? But that's just me. And of course, producers can just reformat things.