Brannew said — in very unambiguous terms — that Mihawk's bounty comes from his strength as the WSS:
"As the strongest swordsman in the world, he is worth 3.59 billion berries!!"
Not:
Mihawk's 3.59B bounty is attributable to one reason and one reason only: his strength as the WSS.
Anything else is baseless headcanon.

"As the strongest swordsman in the world, he is worth 3.59 billion berries!!"
Not:
- "As the Marine Hunter"
- "As an Executive of the Cross Guild"
- "As a rival of Red Haired Shanks"
- "As an associate of Crocodile"
- "As a former Warlord"
- "As a subordinate of Buggy The Clown"
Mihawk's 3.59B bounty is attributable to one reason and one reason only: his strength as the WSS.
Anything else is baseless headcanon.