You might like Yamato, and he's made a strong impression, ticks off a lot of boxes. But he doesn't give me the impression of being a character planned very far in advance, which is one advantage Carrot has in her favor. Oda knew she would be in the war, and planted her into the story and the hearts of the crew years ago. That connection to the crew, both on WCI and now on Onigashima, is another advantage: only Luffy knows of Yamato's existence, which will need to be addressed and doesn't look like it will be anytime soon.
Yamato is emulating Oden to a fault. Is that all he'll ever want to be? Because while the SHs admired and were inspired by their mentors, they are their own selves, and not trying to be someone else. And if Yamato does break out a bit more and try to be his own person, who's to say what he'll decide to do? Maybe traveling the world is something he'd want to do for himself and not just because of Oden, but he also could decide he'd want to stay in Wano with Kaido gone and Momo more accepting of him, especially if he stops trying to replace his dad.
Being relevant is important, and she definitely has a part to play in the future, but it doesn't equate to being an actual SH pirate. Vivi chose to remain a princess and lead her country. She hasn't shown any change in strength, and even if she reunites with the crew at some point, how will she contribute when the others spent two years intensely training?
He should have joined then, but it's the same deal as the end of FI: he had something else he needed to take care of first, and he only signed the contract, so to speak, when he came back for good. His absence from the volume table of contents and all the color spreads for two years supports that.