Bounty isn't an argument. Blackbeard had a bounty of 0 and defeated 550 Mil bounty Ace. Jack got his bounty from devastation.
That's because no one knew about him, but the moment you receive a bounty, it means that you're already known and acknowledged by the government with your actions followed
Doffy got 340 Mil which does not include him being the biggest underworld broker, selling weapons to promote wars, selling artificial Devil Fruits keeping a part of Dressrosa as puppet slaves and in the end wanting to annihilate a whole country.
You could have at least added that his bounty was frozen because he was a shichibukai for long lol. Fact remains however that Jack has the double of the bounty of the guy who defeated him. It can't be a coincidence, especially since it was said it's harder to increase in bounty starting 300millions and that your feats must really be incredible to accomplish it. Just look at Luffy. He had 400millions berry pretimeskip, had 2years of training and reached his limits against Doffy, yet it was only raised up to 500millions(100millions more), yet Jack's bounty is 500millions ahead(the first billions berry bounty in the manga). Kid who has the same mindset was only 15millions ahead of pretimeskip Luffy. His nature alone can't be the only reason behind such a high bounty. Besides to be able to cause devastation you need strength. That's why Kid despite having the same mindset as him didn't even cross the 500millions berry yet(more than half below) simply because unlike Kid, Jack is a danger to even powerful new world islands
You also have to think of it from a story perspective:
- Oda foreshadowed this guy since Punk Hazard
- Sent to capture Raizou in one of the most powerful independant islands
- Dedicated multi-flashback chapters to hype this guy
- Fought one of the most powerful new world islands(Zou) that Luffy who rarely acknowledge someone said was "strong" the moment they met, who are friends to powerful people(Shanks, Marco, etc), are mentioned to be the ones the world is waiting for, are guarding one of the road poneglyphs for 5 days and took no damage
- Left to attack a convoy with 2admirals,1high level VA and their fleet, and still managed to destroy 2 and coming out relatively ok to the point the government had to cover-up by lying that he is dead
- Come back to Zou and decides to kill an island-sized elephant and currently presented as the Zou(Post-Dressrosa arc) antagonist
Oda developed this guy way too much that if he ends up weaker than Doffy, it would not make sense
