Given the "bromance" part of the story and Spock still dealing with his emotions and the loss of his mother and Vulcan, Spock's primal shout of, "Khaaaaan!" is far more appropriate than Kirk's was in TWOK. It's the straw that broke the camel's back. First his mom and Vulcan, and now Kirk? No wonder he goes on a tirade.
The thing that's too bad is so many folks only think of, "Khaaaaaaaan," as some sort of joke. It almost always gets snickers, now. More people probably remember Costanza yelling it on "Seinfeld" than remember it from TWOK.
To me, Spock yelling it seems like it would be one of the most emotionally poignant parts of the movie. It doesn't deserve comparison to the cheesy version, even if the writers invited it. There's far more gravitas this time. It's sincere. It conveys true pain and loathing.