Well why would Vivi want to go on adventures instead of ruling her country? Especially when the WG would threaten Alabasta, not just take control of it. I understand Vivi is the honorary SH but there's a reason she chose to stay instead and it hasn't changed. She's also weaker than pre timeskip Nami still so she wouldn't contribute in any fight in the future.
Yamato mirrors Oden more than Sabo but if I were to grant that, you aren't considering what Sabo's situation is. He has a home of his own with the revolutionary army. He was raised there since childhood and now holds the second most important position. If Sabo wanted to give that up to join the crew, he easily could've done so in Dressrosa and Luffy would gladly take him in. Same thing for Ace back in Alabasta when Luffy directly asked him. He said no because of his current family with the WB pirates so its implied Sabo would do the same. They both just told the crew to take care of their little brother.
How can she rule a country when she’s a wanted criminal. It’s the same logic that made Franky join the crew. And Vivi joined the crew when Alabasta was in danger from crocodile. Now it’s under even greater danger because of Imus vendetta. She can’t simply return.
Why do you think Sabo was specifically written about in the paper? Why do you think no one could get in contact with him from the Revs? Something happened and Sabo’s on the run. If it was simple enough that Sabo could just return to the revs, Koala wouldn’t have been so scared. And Yamato doesn’t mirror Oden, especially not as well as Sabo.
Oden - Born to Nobility but ran away at a young age - Sabo
Oden - Got in constant trouble as a kid - Sabo
Oden - Joined a group of criminals who came to the island in order to escape - Sabo
Oden - Is called a brother of Whitebeard and Roger - Sabo is called a brother of Ace and Luffy
Oda even drew it outright when Luffy stated his true dream as a kid Ace was connected to Whitebeard, and guess who Sabo was connected to? Oden.