Trek is often guilty of giving 'inappropriate' tasks to main characters - I view Spock as primarily a physicist with expertise in Sensors, Maths, and Computing but he often deals with communications issues and engineering issues. Programming the Kobayashi Maru test fits with his character though and he might be delegated the task of assigning cadets because he was most recently involved in assessing them. Like Data you feel that Spock just needs more hours in the day and he could run everything single-handed.
I recall one episode of Voyager where the crew had to go on a geology mission. Instead of introducing a ship's geologist, they picked main characters who had taken geology for one semester and Neelix because he went in a cave once.
As a trained biologist and a qualified medic, Chapel could have gone on loads more away missions than she did.
In 2 hour movies it will be hard to give all the characters interesting and appropriate moments to shine but from the pictures I've seen it does look as though Uhura is going to be given a more prominent role. I hope they give her something to do because she is qualified to do it not because they want the heroine to be in peril or because she's out to help her man.