So I'm not sure why it's important that we see that golden moment they become friends in these movies.
Well, origin story
, ya know. Seeing the origin of one of science fiction's best friendships. It's one of the elements of Harve Bennett's story I rather liked. In that, in very simple terms, it basically goes Kirk helps Spock, Spock helps Kirk, then they help each other in the end. They're not really ever at odds, but they're depicted as unlikely friends because of their different backgrounds.
Though i'd still consider it "wrong" honestly. Simply because I always felt the start of Kirk and Spock's friendship was best established as a course both characters would follow in WNMHGB, and done rather well there too.