Oda decided Mihawk is the WSS not Shanks.You talk like you know more about the manga then Oda, which you don't.
We haven't even seen Mihawk use one name attack and yet you making it sound like we seen his full power.
Champions don't have to prove anything to anyone because they are the champions. Challenges are the ones you have to prove they are worthy to challenge the champion.
You forgot to the most important feat. Mihawk casually strolling into Yonko territory. Approaching the Yonko by himself. The Yonko requesting to dual Mihawk. In other words, the challenger asking the champion if he's worthy enough to challenge him. Mihawk, in front of the Yonko crew, not just deny his request but in a very disrespectful way by calling him a one arm has been. Finally, the Yonko not doing anything about it.