SNW is kind of a fork of TOS, not just a prequel … what were to have happened if the first pilot were picked up. And in that sense, the Spock we’re getting, up until now at least, isn’t just a prequel but a kind of continuation/interpretation of The Cage. Additionally, from The Menagerie, we know Spock had a relationship with Pike … so it’s window of time with an established existence and Spock within it, and, importantly, no real need to depict exactly how and when it transitions into the TOS era … as it’s its own period and can just be.
Kirk is not part of this time, and is very much the center of the TOS period. Adding him is necessarily an act prequel inference that is looking forward toward TOS.
And yea, Uhura, Chapel and M’Benga are different stories. Though I will say I’m not entirely happy that Uhura is in the show for the same reasons, except that in her case she’s not nearly the central character Kirk is in TOS and so basically operates as an independent character.