I doubt that any of the fans nitpicking the movie are aware of any issues with the story that the writers and at least some of the producers were not. They simply made certain choices. So "could we have saved" what is really in most respects quite a good script? No, no we could not.
The movie showed quite a bit of how Kirk and Spock became friends. Old Spock's "I could not deprive you..." speech wasn't instruction to Young Spock, it was offered after the fact by way of explanation for his staying out of the way during much of the story.