Because it’s his story and oda likes him
Most other conquerors just expect for Luffy to show superiority over them
Okay but he has Zoro who is a CoC user and Mihawk is his main target why not pay attention to that connection?
Having a strong devil fruit doesn’t somehow lessen your chances of being a conqueror
Same way having a strong body or weapon doesn’t effect having conquerors or not either
Saying someone can’t or has to have conquerors because they’d be to strong or weak doesn’t make much sense. You’re either a one or you aren’t regardless
You either don't understand me or you don't want to understand me.
Just because you have a fruit doesn't preclude you from having CoC or being a gynetic freak of nature or having all of those things at the same time.
But Admirals currently don't have CoC despite the fact that we've seen enough fight scenes with them. That's not to say they don't have a chance at all to be conquerors or at least some of them but let's be honest they aren't great and the Admirals themselves aren't prime candidates for CoC.
Despite all of that they are recognized tiers in the OP world and are most hyped for their fruits albeit possessing good CoA and CoO.
Given that Mihawk is also a recognized top tier but is a mere human who doesn't have any fruit he is clearly an AdCoC user since we see a pattern that every other top tier like him (Shanks/Ray/Oden and ect) has it.
It is implied he strived for more
That he was just settling when he joined the warlords and when he and crocodile teamed up
Also zoro’s dream to be the wss is bigger than him just doing it because he wants to be strong. He’s doing it not just for himself but to help kuina and luffy achieve their dreams. Zoro’s ambitions > mihawks
Okay I can agree that Mihawk could/could have had a bigger goal that he didn't achieve but that doesn't change the fact that:
1. Mihawk himself thinks he's sitting on top.
2. It's pretty explicitly stated in the story that WSS=King.
3. The Mihawk/Zoro and Roger/Luffy parallel.
If we take it further, we can assume that Roger also didn't achieve his bigger goal since he wasn't Joy Boy but he has CoC.
Just because Mihawk didn't become something more big doesn't negate the fact that he is already the King Swordsman and sits at the top.
It's simple.