Going back to Arlong park, Luffy said he isn't good at things, (including muh sword) but he is good at being strong. Reread ch 90.
One aspect of the pirate king is strength, you can have near equivalent strength to the PK but be lacking in allies, resources and ambition and so be a silver medalist like whitebeard, but strength is a big component also. Mihawk isn't even oldbeard tier let alone PK tier.
Just like Rayleigh protected Roger by fighting Rocks and WB for him... oh wait you are full of shit. Where was Zoro's protection against Lucci, Crocodile, Doflamingo? - Against the subordinates, Zoro's main role is to fight the strongest or second strongest subordinate of the enemy.