That would be terrible writing on the part of Oda for Zoro. He was the one who told Luffy he needed to get real and act as the New World demands. For him to just sit by if Luffy is clearly getting closer to dying with no sign of him pulling it off, just going ¨Nah, he'll do it¨ would be contradictory and regressive, especially after the incident with Kuma and being the one who reminded the crew that being pirates wasn't some kiddy game.
Law is putting his faith in Luffy because he's currently incapacitated. If he's revived, he will definitely be joining in again. Fujitora is someone who would stop Doffy if Luffy fails.
CP0 may be on the island, we don't know if they left so they're still a possibility.
Sabo may still end up on where Luffy is.
He already showed plenty of times during this manga whether in Enies Lobby, Thriller Bark or Dressrosa that he has complete faith on his captain. In Dressrosa he even told the giant that by the time he will wake up, the cage will disappear. It's because he trusts Luffy's strength to think it's enough to deal with Doflamingo. In his mind, Doflamingo isn't that great of a threat and Zoro is the example type of a guy who will never try to go against the captain's orders. He always try to follow them acknowledging them as the captain's decisions and shield him against anything that will go in his way. That is his usual job, his usual way of thinking and since Luffy already said he would deal with Mingo, he already put his faith in his captain to be able to do so, because he respects the captain's position and trust Luffy's strength more than anyone else.
Though i could agree that in this particular situation, he should go because Viola reported Law has fallen with Trebol and Doflamingo around, so he should probably know that at this point, someone is getting in the way of his captain's battle(Trebol), which could put him in a dangerous situation. He even seemed rather shocked to hear Law was defeated, so with all this, he probably feels Luffy is threatened, at least it's how i think he should be, so it'd be weird if he didn't try to do anything.
I think however that Oda will probably use the distance issue as an excuse. He did make Zoro go over the other side of the island or so. Sabo who is nearby was even saying it's too far from the palace. But considering that he himself is trying to join it regardless, i suppose Zoro should be able to catch up in time especially with Kanjuro around who should be able to produce birds making the trip faster(assuming Zoro learn about this ability of his, somehow)
Either that or it would have something to do with the birdcage. Maybe Zoro will feel the need to protect the place while noticing that it shrinks by the time Doffy gets dealt with by Luffy
Maybe but since the beginning of this arc, it has always resolved around the fact Law trusted Luffy too much, with everyone betting on Luffy including an admiral. Since the beginning of this arc, other than the fight versus Chinjao, Luffy didn't shine that much, especially comparatively to Law. I think it's his time to shine and no one deserves to get in his way. He should defeat Doflamingo alone