Among the Yonko, Kaido is the weakest and most vulnerable to being overthrown. This is not to say that Kaido himself is weak, but that his organization is very flawed and fragile.
- Whitebeard. During Marineford we saw that Whitebeard has divisions with their own individual crews as well as a diverse network of allies. The Whitebeard Pirates and the allies claimed territory by basically forming a [benevolent] protection racket. The New World islands do not get hassled by pirates or other threats and in return, they swear allegiance to Whitebeard. I’m not exactly sure what the Whitebeard Pirates got out of their protection racket. Whitebeard desired a family and the islands that his crew protected are an extension of this family. Unlike Big Mom or Kaido, the Whitebeard Pirates didn’t demand anything unreasonable and didn’t wantonly destroy islands for failing to deliver–that we know of anyway. So, being under Whitebeard’s wing was pretty nice, all things considered, and this mutual goodwill formed a force that rivaled the entire Marine HQ.
- Blackbeard. We haven’t seen enough of him to say much. He likely emulated Whitebeard’s structure, minus the benevolence. He desires power above all else and will not hesitate to use that to rule. Same protection racket, different motivation, probably fear instead of goodwill. Knowing Blackbeard, he would probably destroy deserters to prevent them going to the other Emperors.
- Big Mom. She has the most formal structure of all the Emperors we have seen so far. Her kingdom really is a kingdom with “bureaucrats” to collect taxes (life force) and “ministers” to rule individual “departments” (islands). Aside from Big Mom being mentally ill and prone to destructive hunger pangs, her rule was not so bad unless you decided to leave, then you would have to give up your lifespan, be maimed, or killed outright. Her rule isn’t benevolent, but at least her children’s rule are overall on the positive side as they show concern for their kingdom and the citizens actually like Big Mom’s ministers. Just don’t leave!
- Kaido. What does Kaido desire aside from being Pirate King and claiminig the One Piece? He loves to fight and it seems like all he wants is to have a huge battle where everything gets trashed. Accordingly, his crew is composed of individuals who got where they are by being stronger than anyone below them. Kaido’s motivation for becoming Pirate King and finding One Piece is simply chaos. The Emperors, World Government, Warloads, Marines–all of them are forced to fight instead of being countered in a delicate balance. He probably hates this balance. Likewise, he demands that his territories produce weapons for war and violence. Far from being a protection racket, Kaido actively exploits and oppresses his territories (Wano). This foundation is very weak and as we found out, the people want to be free and will fight for it. If Kaido goes down, no one can replace him and his territories/allies will defect en masse–huge free-for-all for all the other players. In a way, the Straw Hats are doing Kaido a solid favor, there will be chaos and fighting and Kaido will be responsible. The difference is that the exact cause is his defeat and not his win. Still, I don’t think he’s gonna “die” and he might even appreciate Luffy later since someone finally broke the balance. He’ll stick around for the chaos.
So one takeaways is that the Straw Hat Alliance’s victory over the Beasts Pirates is pretty logical and expected. The Beasts Pirates aren’t great at functioning as an organization nor as a team, and if you have enough raw strength and some strategy, you can overcome them and topple Kaido’s empire in one swoop. Blackbeard and Whitebeard would be next on the difficulty scale, as both relied on a very strong leaders/symbols to rally around. Defeating the Big Mom Pirates would take the most time/effort as there is literally a national military that can continue to function with or without her (minus the soul-powered soldiers). Yet, our protagonists have seen a shortcut strategy: let Big Mom destroy her own kingdom out of insanity. Nevertheless, I think they will be allies or mutually non-aggressive once Luffy treats Linlin’s mental illness. That or Sanji will create a delicious dessert whenever she goes crazy to bribe her and her children, thus solving the Big Mom Pirates’ longstanding stability problem.
As for Shanks… my guess is that he has a mixture of all the above plus tacit support from World Government/Marines.
Shanks probably made a deal with the World Government to claim territories and in return, World Government and Marines will refrain from disrupting the power balance. Shanks is portrayed as a good guy… but what does he really want? The Red Hair Pirates are such an unknown, I can’t wait for their full reveal!