correct me if i am wrong the story has stated two kingly ambitions...1.pirate king and 2.worlds strongest swordsman right??? At this point thats all the confirmation needed for mihawk to have it. Mihawk just like zoro had a kingly ambition because zoro had this ambition he gets coc, and oda lets him get adv coc. Mihawk on the other hand had the same goal as zoro but he attained that goal and sits at the top of all swordsmen...it would be absolutely weird and inconsistent for the swordsman that sits atop all others to lack the ability that a handful of the very strongest are using unless you are making the argument that black blades are stronger than adv coc,but then it seems weird for oda to give zoro both adv coc and black blades he should have just gave him black blades and thats it.
Mihawk have 0 king ambitions .
He just ended up there because he was stronger then the other swordmans he fought .
He is bored and don't want be important because its a bother .
I don't think mihawk ever wanted be the worsld strongest swordman he just is .
If I remember well tehy give him the title after he defeat all the swordmans challenging him .
He is like king in one punch man he got the title gift to him without consent but accept it anyway because he got good fights from it .
NO its not weird because zoro will surpass mihawk