If you think WSS is Mihawk's Goal, why Mihawk is a pirate? He shouldn't have been a pirate if his goal was just WSS. You can be WSS without being a pirate.
If some of you remember, there are some mihawk and Lolo fans were saying that mihawk is not a pirate, but in the end we've seen Larines are chasing mihawk right after mihawk lost his Shichibukai title, because as we were right that mihawk is a pirate
before and after,
We also see mihawk in Roger's execution and it's possible just like Doflamingo, moria and Crocodile, mihawk too was impressed with Roger, and become a pirate because of that, that's the only clue about mihawk being a pirate, because of Roger.
And same mihawk admitted that surpassing his level is still not enough to be on Roger's level,
Mihawk : ''What is your goal?''
Luffy : ''To be King of Pirates !''
Mihawk : ''Even more perilous than trying to surpass me.''
--- Chapter 0052
mihawk basically said; Roger's level > surpassing mihawk's level > mihawk's level.
We never see pirates having WSS goal. Lolo is only a pirate because Luffy forced him to be one.
Lolo is a special case because of Luffy, we don't know why mihawk is a pirate yet, we can only guess why he become one, and it's obvious mihawk don't have any captain so he was definitely not forced to be a pirate like Lolo was. You don't need to be a pirate to be a swordsman.
Mihawk is a pirate, and in the pirate hierarchy he is definitely weaker than ''Great'' Pirates, since Mihawk is a pirate.
This is just like lets say Vice-Admiral Momonga become the WSS but not an Admiral at the same time due to not seeing worthy for that position by his superiors, then saying that Momonga > Fujitora based on WSS title.
If mihawk is superior to Shanks, first of all, mihawk would definitely be listed as a ''great'' pirate, because mihawk is foremost a pirate
, and mihawk would've more accomplishments as a pirate rather than being WSS, he is a pirate after all, mihawk's accomplishment as a pirate is being a Shichibukai. That's it.
And another thing is, mihawk never said his goal is WSS, its just people calls him, and in Lolo novel, people said Vista or Shanks, and even Dressrosa Lolo might be WSS over mihawk.
It's not even a certain title, what certain is mihawk is a pirate, and he is below Great Pirates such as Yonko. If Kaido or Shanks loses their crew, they would be still listed as 'Great Pirates' , not just some Shichibukai Pirate.
Pirate mihawk not having a crew is not an excuse because he chooses not to have a crew and be a pirate at the same time.
Shanks as a Great pirate is superior to mihawk as a pirate.
People who consider mihawk as Shanks's superior due to some sword title, don't consider the fact that they are both pirates
, and Shanks is mihawk's superior as a pirate.
I think you should consider;
A- mihawk is a pirate, both are, and he is below Shanks since Shanks is a great pirate
, mihawk is not a great pirate.
B- mihawk said Lolo's cause to help Luffy to be PK is greater than the WSS ambition, so this doesn't necessarily mean their goals and their ambitions are equal, mihawk admits Lolo is aiming for something greater than WSS.
Mihawk: ''It would seem that you've found a greater cause than your own ambition.''
--- Chapter 0597