It works for me as a character-building thing. On the one hand, Spock has real emotional needs that can't be met by anyone else; he's too Vulcan to be accepted by humans and too human to be accepted by Vulcans so he faces social isolation from all but his closest friends (and sometimes even from them). On the other hand, Uhura strives to understand him and his way of being, doesn't judge him for it, and finally comes to accept and even appreciate it. This is something Spock Prime never really had: always dignified, always in control, always healthy and well-adjusted in working with his peers, but always, in the end, alone.
I've pointed out many times that ST09 had to update Star Trek's characterizations to deal with generational differences from the 60s. The retread of Kirk was a nod to the Fail Generation: kids and young adults who grew up surrounded by crumbling institutions offering a promise of mediocrity if they work their asses off and prison time if they don't. Christopher Pike tells Kirk "You can settle for a less-than-ordinary life, but you feel like you were meant for something better, something special." That line wasn't just meant for Kirk.
Spock/Uhura deals with the more intimate aspects of that generation from a lot of different angles at once. Spock is a highly talented person with extremely poor emotional intelligence; that's a blind spot for him, but for Uhura it's not a deal breaker. At the same time, he's a product of a social tug-of-war between two competing ethnicities that don't always (or even usually) get along together.
The running theme of the reboot movies is the Pursuit of Acceptance. Kirk is looking to achieve his full potential and be accepted as a professional; Spock, who is already a well-respected professional whose qualifications were never in doubt, wants to be accepted as a person. And they both find what they're looking for on the bridge of the Enterprise.