Well, Alexander should serve as liaison between the Klingons and the Federation, so he was needed on the Bortas first to keep Kromm in check, who was not so happy to work with a Federation captain to "preserve the peace". (Also the "Aventine" was desperately needed by John Jackson Miller's novel "Takedown".
)
And yes Spock doesn't leave the prime universe before 2387.

And yes Spock doesn't leave the prime universe before 2387.