Oda himself said that yonko commanders get a bounty raise based on their captain. Kaido and his crew actively destroy countries and wreak havoc, but BM prefers business.
1. That's not what Oda said. Oda simply said that being under an emperor has an impact on the bounty, nothing about their whole bounties being based on their captains. Since you're using this statement by Oda, let's also look at the example he used to express this statement:
Strawhat pirates who didn't participate in the battle at Dressrosa getting a bounty increase of 50 mil, after Luffy goes up to 500 mil. A very small amount.
Then in the manga created by that same Oda who made that statement we come to post-WCI, Luffy's bounty has been increased by 1 billion, standing at 1.5 billion. Luffy is now also recognized as an emerging Emperor of the sea. What is the bounty raise given to the strawhats not present there? None. Why? Because bounties are pretty much all based on individual achievements, with a minor part being something else. You guys however have turned that minor part into a major part of their bounties.. which is simply not the case.
2. Since you're bringing up the captains and bounties based on that.. Let's go over that then:
Bounty gap between Kaido & Big Mom: 223 mil
Bounty gap between Kaido's YC2 & Big Mom's YC1: 263 mil
Already a higher bounty gap between than the Captains, and we haven't even gotten to Kaido's "YC1", who's bounty is likely to be fairly higher than Queen's. Now let's look at a diff bounty gap:
Bounty gap between Kaido & Shanks: 600 mil
Who's crew is it that's hyped up to have people with high bounties all across? Shanks
So with both examples we have a clear representation of the Captain's bounty having absolutely no correlation to the bounty of the individuals below them. So with this, I assume you would then want to move to the "wrecks havoc and destroys country" with a claim that it's diff than just how high the captain's bounty is.. So.. let's move to that.
3. Big Mom Pirates & The Beast Pirates..
- Big Mom Pirates are introduced as people who destroy nations simply because the nation didn't deliver candy on time or in good amount. With threatening to destroy FMI. Strengthened again when bobbins reports to Big Mom they destroyed the country because they failed to deliver...
vs
- Beast Pirates are introduced as people who destroy nations because they have a target they need. With Jack's introduction of putting down the Zou because he was sure the Dukes were lying and hiding Raizo there.
Now who's exactly more dangerous, somebody who destroys countries for something as insignificant as candy or somebody who destroys nations to find a target believed to be a threat to them? Not a whole lot of difference is there now.. in fact Big Mom looks like the more savage one here if anything.
Who's the one that's introduced with having strong connections to the underworld?
Big Mom
Who's introduced with having intelligence all over the world to a point she can take out a target in east blue if she wanted? Big Mom
Who has a bigger army in numbers? Big Mom
Kaido's forces on the other hand and actions are fairly limited to Wano and just building up.. and aren't even as big as Big Mom Pirates.
The only real reason why people believe Beast Pirates are somehow more "savage", "actively destroy countries", "cause havoc".. is literally because of the fact they're animals, thus have a "savage" image to them.. The fact is Big Mom Pirates do equal if not worst shit than the beast pirates.
4. Let's look at the subjects at hand here, Jack and Katakuri:
Role-
-> What is Katakuri's role in the Big Mom pirates? Directly under Big Mom, with all of his siblings looking up to him.
-> What is Jack's role in the Beast Pirates? Gets bullied by King and Queen, with being the strongest after them. Not even close to being Kaido's next in command.
Based on the fact that Big Mom pirates do equally if not worst shit than the Beast Pirates, and Big Mom & Kaido are viewed as Cat & Dog.. The bounty of Big Mom's next-in-command should be higher, as he's right under Big Mom to command such a giant organization. But rather he only has 57 mil higher than a guy who is nowhere close to being the same role as Katakuri in his respective crew.
Experience-
Big Mom has been an emperor for 2 decades now, where Katakuri would've been around 28 if we're just limiting it to hardline of BM being an emperor for only 20 years max. We also saw in his flashback, he's been fighting since he was a youngin, and wanted to be a protector for his fam since young age. Considering the likes of Marco/Shanks were fighting in their 15s-17s already, Katakuri should be in a similar situation. Which would give Katakuri at the very least 30 years of experience as a pirate.
On the other hand you have Jack who is just 28 now, at most he has around 15-17 years of experience as a solid pirate fighting. Half of Katakuri's.
Yet despite Katakuri having at-least a decade + of experience over Jack as a pirate, he's only 57 mil above him.
The conclusion of this would be:
Jack in 28 years of his life, has accomplished about nearly as much Katakuri with his 48 years.. when it comes to Piracy.
So all of the things are in Katakuri's favor. A bigger role in nearly an equal dangerous organization as the Beast Pirates. Vastly more experience on the seas than Jack.. Yet only a near irrelevant amount of 57 mil gap between him and Jack.
What does Katakuri have that Jack doesn't, that creates this giant gap between them in the brains of the fandom? A 20 chapter fight with the Main Character.
5. If you want to tell fans not use bounties or bounties are irrelevant to strength calculations for the YCs.. then it's best to tell Oda for that:
He has constantly used bounty when it comes to the commanders to hype up their strength. Even the red-haired pirates. It doesn't make sense when people supporting Katakuri complain about usage of bounty to judge strength.. when half of Katakuri's big hype in the manga was "1 billion beri man". Yet you are trying to tell me it's irrelevant. That doesn't go with the mangaka's intentions based on the constant usage of bounty for the Yonko Commanders and their strength.