I think the "problem" is more that the movie needed to use these characters, as the writers felt the "franchise demanded" this. For the same reason, Kirk becomes Captain of the Enterprise at the end, and so on. The movie does beat you over the head with a huge "these characters are important!!!!!!" sign a little bit.
Had this been a completely new story, the transporter chief would have been the hero instead of Chekov (or Chekov would have been at that position to begin with), and Kirk would have gotten his medal and then been promoted to Lieutenant at the end under thunderous applause. I call this "natural" character development. Others would perhaps call it "organic".
The Phantom Menace had a similar problem. I liked Qui Gon and Darth Maul, but they had to die because the franchise kind of dictated it.