I don't think it'd be out of bounds to assume that in the primary timeline, Spock never had anything to do with the Kobayashi Maru scenario, mainly because he was already out serving on the Enterprise with Pike, at the point in the altered timeline where we see Spock serving as an Academy instructor and taking part in the programming of the simulation (probably a revised version, since back in the original timeline, Kirk took the test a good five years earlier, again, while Spock was either getting ready to graduate himself, or had already shippped out with the Enterprise).
It's also possible that the KM simulation is considered extra credit towards command qualification; not required to get a command, but it looks really good on the transcript, and shows just how badly you want the center chair. Spock never took it, and never was anybody's first choice for a command opening, whereas Kirk took the thing three times, beating it once (probably more of making a statement than anything else), and he made Captain by the age of 30.
It's also possible that the KM simulation is considered extra credit towards command qualification; not required to get a command, but it looks really good on the transcript, and shows just how badly you want the center chair. Spock never took it, and never was anybody's first choice for a command opening, whereas Kirk took the thing three times, beating it once (probably more of making a statement than anything else), and he made Captain by the age of 30.