Her being Spock's foster-sister is mostly backstory in the first season. Her story arc is about redeeming herself to the eyes of Starfleet. Spock and his family don't have to do with The Story of Redemption.
And then Burnham ended up caught as a pawn in Georgiou and Lorca's personal war in the Mirror Universe. Again, nothing to do with Spock or his family.
I agree with the gist of what you said here, though I don't think we'll see Spock much. But at least they're going out of their way to not have TOS Spock.
Maybe this is what it boils down to. If someone's not interested in Culber, Burnham, L'Rell... and by extension Saru, Tyler, Georgiou, Stamets, Tilly, and Cornwell.... then they're going to start focusing more on the TOS characters: Sarek, Pike, Mudd, and I guess Spock.
I'm interested in Burnham, L'Rell, Georgiou, Stamets, and Tilly's arcs. Saru to a lesser extent. And Cornwell when she shows up.
Culber, ehhh.... I don't know. I'm in the camp who's not too sure about this.
I forgot about Georgiou. I am actually looking forward to seeing what she gets up to. Regardless of how much or little screen time they get I'll always enjoy anything on offer from Tilly and Stamets.