He matters to the story bc he trained one of the MC and is buddy with another top tier
The story of one piece is the story of good vs evil. It’s freedom vs authoritarianism. It’s Destiny, inherited will.
where does Mihawk fit into any of the above? Is Mihawk a champion of freedom? No, he willingly worked for the WG. Is he a champion of authoritarianism, no, he’s own working for buggy.
Is Mihawk a good guy? Not really, he’s destined to have a a life and death match with one of the MCs and he doesn’t care that potentially killing Zoro could be bad for the world since Zoro is on the pirate king crew. Is Mihawk a bad guy? Not really since the story has never created a moral reason he should be defeated
is Mihawk connected in anyway to the Destiny piece? Nika lore? Ancient kingdom lore? Df lore? The will of D? The one piece? No, no no no no… It’s Buggy that’s connected to the One piece and mihawk is carried along by Gags
In another manga with another author something very interesting could be done with this. A character directly placed outside of the machinations of the plot everyone else is embroiled in. But this is One piece, and this is Oda. Plot is KING in One piece and Mihawk being the most powerful character DIRECTLY unconnected to any plot means Mihawk is the most powerful USELESS character in the story.
that’s why Oda is fine having Mihawk be a gag subordinate to Buggy, in no world would Oda do this to any other top tier, no admiral, or Yonko would ever be made a gag under Buggy. Even The gag Big mom wouldn’t be out through this because at least she wants the one piece so she matters to the plot.