He has been consistently fighting Kizaru, that is 100% his fight. And frankly if Saturn is the bigger threat presumably then theres no way Zoro takes over that fight either.
You acknowledge the AR is likely here to stave off that battle and make it a 2v2, this is what Oda does, his prerogative is to make Luffy the center of attention in these conflicts.
If Saturn were a raid battle where Zoro would join then I wouldnt have expected Sanji to leave the scene either, yet here he did.