Except thry made a point in ID that the five year mission was a one-of-a-kind thing into uncharted territory, which the Enterprise was picked for.
Then again, the old Enterprise bumped into dozens of Federation ships and was meant to be on the same five year mission. Just one of those tropes, I guess.
Which often led to stories of a) the good intentions of someone gone awry, e.g. "Patterns of Force", b) accidentally affecting of a culture, e.g. "A Piece of the Action", or c) captains gone rogue, e.g. "The Omega Glory". In any case, Kirk and company had to make things right. So maybe STB is an A, B, or C type of story (and of course "D" must be offered, because "none of the above" should always be a choice).
Maybe D is "Bread and Circuses". Combine a ST film with some fast-paced, in-your-face CGI gladiator action. Sounds like a win-win for the studios.
Well, Maybe if John Logan had been the co-writer with Pegg ....