As far as I understand the friendship criticism, it was not that they're simply friends. It was because in the first movie they were pretty much rivals, and in this movie it's progressed to a point where Spock is screaming "Khaaaaaaan" after Kirk's death (which does seem somewhat abrupt and even out of character). The critique says that these movies are relying on a lot of the previously established lore to provide that gradually established familiarity between the two, rather than building that relationship on its own. If the two movies stood alone, it's harder to believe Spock and Kirk becoming friends given how adversarial they were toward each other and given their personalities. Yeah, maybe they became friends working together in the year we didn't see, but the point there is that we didn't see it.